bluuebunny/crossref_metadata_2025 huggingface dataset:
Composition operators between algebras of differentiable functions
Authors: Gutiérrez Joaquín M. , Llavona José G.
Published: June 2012

Let

E
E

,

F
F

be real Banach spaces,

U
⊆
E

U \subseteq E

and

V
⊆
F

V \subseteq F

nonvoid open subsets and

C
k

(
U
)

{C^k}(U)

the algebra of real-valued

k
k

-times continuously Fréchet differentiable functions on

U
U

, endowed with the compact open topology of order

k
k

. It is proved that, for

m
≥
p

m \geq p

, the nonzero continuous algebra homomorphisms

A
:

C
m

(
U
)
→

C
p

(
V
)

A:{C^m}(U) \to {C^p}(V)

are exactly those induced by the mappings

g
:
V
→
U

g:V \to U

satisfying

ϕ
∘
g
∈

C
p

(
V
)

\phi \circ g \in {C^p}(V)

for each

ϕ
∈

E
∗

\phi \in {E^\ast }

, in the sense that

A
(
f
)
=
f
∘
g

A(f) = f \circ g

for every

f
∈

C
m

(
U
)

f \in {C^m}(U)

. Other homomorphisms are described too. It is proved that a mapping

g
:
V
→

E

∗
∗

g:V \to {E^{\ast \ast }}

belongs to

C
k

(
V
,
(

E

∗
∗

,

w
∗

)
)

{C^k}(V,({E^{\ast \ast }},{w^\ast }))

if and only if

ϕ
∘
g
∈

C
k

(
V
)

\phi \circ g \in {C^k}(V)

for each

ϕ
∈

E
∗

\phi \in {E^\ast }

. It is also shown that if a mapping

g
:
V
→
E

g:V \to E

verifies

ϕ
∘
g
∈

C
k

(
V
)

\phi \circ g \in {C^k}(V)

for each

ϕ
∈

E
∗

\phi \in {E^\ast }

, then

g
∈

C

k
−
1

(
V
,
E
)

g \in {C^{k - 1}}(V,E)

.
Certain hypergeometric series related to the root system 𝐵𝐶
Authors: Beerends R. J. , Opdam E. M.
Published: June 2012

We show that the generalized hypergeometric function2F1_2{F_1}of matrix argument is the series expansion at the origin of a special case of the hypergeometric function associated with the root system of typeBCBC. In addition we prove that the Jacobi polynomials of matrix argument correspond to the Jacobi polynomials associated with the root system of typeBCBC. We also give a precise relation between Jack polynomials and the Jacobi polynomials associated with the root system of typeAA. As a side result one obtains generalized hook-length formulas which are related to Harish-Chandra’sc{\mathbf {c}}-function and one can prove a conjecture due to Macdonald relating two inner products on a space of symmetric functions.
Fragments of bounded arithmetic and bounded query classes
Authors: Krajíček Jan
Published: June 2012

We characterize functions and predicates

Σ

i
+
1

b

\Sigma _{i + 1}^b

-definable in

S
2
i

S_2^i

. In particular, predicates

Σ

i
+
1

b

\Sigma _{i + 1}^b

-definable in

S
2
i

S_2^i

are precisely those in bounded query class

P

Σ
i
p

[
O
(
log
⁡
n
)
]

{P^{\Sigma _i^p}}[O(\log n)]

(which equals to

Log

Space

Σ
i
p

\operatorname {Log}\;{\text {Space}}^{\Sigma _i^p}

by [B-H, W]). This implies that

S
2
i

≠

T
2
i

S_2^i \ne T_2^i

unless

P

Σ
i
p

[
O
(
log
⁡
n
)
]
=

Δ

i
+
1

p

{P^{\Sigma _i^p}}[O(\log n)] = \Delta _{i + 1}^p

. Further we construct oracle

A
A

such that for all

i
≥
1

i \geq 1

:
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper P Superscript normal upper Sigma Super Subscript i Super Superscript p Superscript left-parenthesis upper A right-parenthesis Baseline left-bracket upper O left-parenthesis log n right-parenthesis right-bracket not-equals normal upper Delta Subscript i plus 1 Superscript p Baseline left-parenthesis upper A right-parenthesis">

P

Σ
i
p

(
A
)

[
O
(
log
⁡
n
)
]
≠

Δ

i
+
1

p

(
A
)

{P^{\Sigma _i^p(A)}}[O(\log n)] \ne \Delta _{i + 1}^p(A)

. It follows that

S
2
i

(
α
)
≠

T
2
i

(
α
)

S_2^i(\alpha ) \ne T_2^i(\alpha )

for all

i
≥
1

i \geq 1

. Techniques used come from proof theory and boolean complexity.
Inequalities for mixed projection bodies
Authors: Lutwak Erwin
Published: June 2012

Mixed projection bodies are related to ordinary projection bodies (zonoids) in the same way that mixed volumes are related to ordinary volume. Analogs of the classical inequalities from the Brunn-Minkowski Theory (such as the Minkowski, Brunn-Minkowski, and Aleksandrov-Fenchel inequalities) are developed for projection and mixed projection bodies.
Some complete Σ¹₂ sets in harmonic analysis
Authors: Becker Howard , Kahane Sylvain , Louveau Alain
Published: June 2012

We prove that several specific pointsets are complete

Σ
2
1

\Sigma _2^1

(complete PCA). For example, the class of

N
0

{N_0}

-sets, which is a hereditary class of thin sets that occurs in harmonic analysis, is a pointset in the space of compact subsets of the unit circle; we prove that this pointset is complete

Σ
2
1

\Sigma _2^1

. We also consider some other aspects of descriptive set theory, such as the nonexistence of Borel (and consistently with

ZFC

{\text {ZFC}}

, the nonexistence of universally measurable) uniformizing functions for several specific relations. For example, there is no Borel way (and consistently, no measurable way) to choose for each

N
0

{N_0}

-set, a trigonometric series witnessing that it is an

N
0

{N_0}

-set.
Geometry of weight diagrams for 𝑈(𝑛)
Authors: Tan Eng-Chye
Published: June 2012

We study the geometry of the weight diagrams for irreducible representations of

U
(
n
)

U(n)

. Multiplicity-one weights are shown to have nice geometric characterizations. We then apply our results to study multiplicity-one

K
K

-types of principal representations of

U
(
n
,
n
)

U(n,n)

.
Global phase structure of the restricted isosceles three-body problem with positive energy
Authors: Meyer Kenneth , Wang Qiu Dong
Published: June 2012

We study a restricted three-body problem with special symmetries: the restricted isosceles three-body problem. For positive energy the energy manifold is partially compactified by adding boundary manifolds corresponding to infinity and triple collision. We use a new set of coordinates which are a variation on the McGehee coordinates of celestial mechanics. These boundary manifolds are used to study the global phase structure of this gradational system. The orbits are classified by intersection number, that is the number of times the infinitesimal body cross the line of syzygy before escaping to infinity.
The nef value and defect of homogeneous line bundles
Authors: Snow Dennis M.
Published: June 2012

Formulas for the nef value of a homogeneous line bundle are derived and applied to the classification of homogeneous spaces with positive defect and to the classification of complete homogeneous real hypersurfaces of projective space.
Stability and dimension—a counterexample to a conjecture of Chogoshvili
Authors: Sternfeld Yaki
Published: June 2012

For every

n
≥
2

n \geq 2

we construct an

n
n

-dimensional compact subset

X
X

of some Euclidean space

E
E

so that none of the canonical projections of

E
E

on its two-dimensional coordinate subspaces has a stable value when restricted to

X
X

. This refutes a longstanding claim due to Chogoshvili. To obtain this we study the lattice of upper semicontinuous decompositions of

X
X

and in particular its sublattice that consists of monotone decompositions when

X
X

is hereditarily indecomposable.
On the existence and uniqueness of solutions of Möbius equations
Authors: Xu Xingwang
Published: June 2012

A generalization of the Schwarzian derivative to conformal mappings of Riemannian manifolds has naturally introduced the corresponding overdetermined differential equation which we call the Möbius equation. We are interested in study of the existence and uniqueness of the solution of the Möbius equation. Among other things, we show that, for a compact manifold, if Ricci curvature is nonpositive, for a complete noncompact manifold, if the scalar curvature is a positive constant, then the differential equation has only constant solutions. We also study the nonhomogeneous equation in an

n
n

-dimensional Euclidean space.
Reflecting Brownian motion in a cusp
Authors: DeBlassie R. Dante , Toby Ellen H.
Published: June 2012

Let

C
C

be the cusp

{
(
x
,
y
)
:
x
≥
0

\{ (x,y):x \geq 0

,

−

x
β

≤
y
≤

x
β

}

- {x^\beta } \leq y \leq {x^\beta }\}

where

β
>
1

\beta > 1

. Set

∂

C
1

=
{
(
x
,
y
)
:
x
≥
0
,
y
=
−

x
β

}

\partial {C_1} = \{ (x,y):x \geq 0, y = - {x^\beta }\}

and

∂

C
2

=
{
(
x
,
y
)
:
x
≥
0

\partial {C_2} = \{ (x,y):x \geq 0

,

y
=

x
β

}

y = {x^\beta }\}

. We study the existence and uniqueness in law of reflecting Brownian motion in

C
C

. The angle of reflection at

∂

C
j

∖
{
0
}

\partial {C_j}\backslash \{ 0\}

(relative to the inward unit normal) is a constant

θ
j

∈

(

−

π
2

,

π
2

)

{\theta _j} \in \left ( { - \frac {\pi } {2},\frac {\pi } {2}} \right )

, and is positive iff the direction of reflection has a negative first component in all sufficiently small neighborhoods of

0
0

. When

θ
1

+

θ
2

≤
0

{\theta _1} + {\theta _2} \leq 0

, existence and uniqueness in law hold. When

θ
1

+

θ
2

>
0

{\theta _1} + {\theta _2} > 0

, existence fails. We also obtain results for a large class of asymmetric cusps. We make essential use of results of Warschawski on the differentiability at the boundary of conformal maps.
𝐸𝐻𝑃 spectra and periodicity. I. Geometric constructions
Authors: Gray Brayton
Published: June 2012

The techniques used in

E
H
P

EHP

calculation are studied, and lead to the notion of an

E
H
P

EHP

spectrum. A simple inductive procedure suggests the existence of higher order

E
H
P

EHP

spectra in which the first differential corresponds to

v
n

{v_n}

multiplication. The next case

(
n
=
1
)

(n = 1)

is constructed using the work of Cohen, Moore, and Neisendorfer. Some of the expected universal properties are proven.
𝐸𝐻𝑃 spectra and periodicity. II. Λ-algebra models
Authors: Gray Brayton
Published: June 2012

The results of part I suggest that for small

m
m

, the Smith-Toda spectrum

V
(
m
)

V(m)

can be approximated by spaces having universal mapping properties and interlocking fibrations. For each

m
m

, a

Λ
\Lambda

-algebra model representing the Bousfield-Kan

E
′

E\prime

term for these spaces is constructed, and all of the ideal results are proven on the chain level.
𝐾-theory of Eilenberg-Mac Lane spaces and cell-like mapping problem
Authors: Dranishnikov A. N.
Published: June 2012

There exist cell-like dimension raising maps of

6
6

-dimensional manifolds. The existence of such maps is proved by using

K
K

-theory of Eilenberg-Mac Lane complexes.
On the Toda and Kac-van Moerbeke systems
Authors: Gesztesy F. , Holden H. , Simon B. , Zhao Z.
Published: June 2012

Given a solution of the Toda lattice we explicitly construct a solution of the Kac-van Moerbeke system related to each other by a Miura-type transformation. As an illustration of our method we derive theNN-soliton solutions of the Kac-van Moerbeke lattice.
Prescribing scalar curvatures on the conformal classes of complete metrics with negative curvature
Authors: Jin Zhi Ren
Published: June 2012

Let

(

M
n

,
g
)

({M^n},g)

be a complete noncompact Riemannian manifold with the curvature bounded between two negative constants. Given a function

K
K

on

M
n

{M^n}

, in terms of the behaviors of

K
K

at infinite, we give a fairly complete answer to when the

K
K

can be the scalar curvature function of a complete metric

g
1

{g_1}

which is conformal to

g
g

.
Symmetries of planar growth functions. II
Authors: Floyd William J.
Published: June 2012

Let

G
G

be a finitely generated group, and let

Σ
\Sigma

be a finite generating set of

G
G

. The growth function of

(
G
,
Σ
)

(G,\Sigma )

is the generating function

f
(
z
)
=

∑

n
=
0

∞

a
n

z
n

f(z) = \sum \nolimits _{n = 0}^\infty {{a_n}{z^n}}

, where

a
n

{a_n}

is the number of elements of

G
G

with word length

n
n

in

Σ
\Sigma

. Suppose that

G
G

is a cocompact group of isometries of Euclidean space

E

2

{\mathbb {E}^2}

or hyperbolic space

H

2

{\mathbb {H}^2}

, and that

D
D

is a fundamental polygon for the action of

G
G

. The full geometric generating set for

(
G
,
D
)

(G,D)

is

{
g
∈
G
:
g
≠
1

\{ g \in G:g \ne 1

and

g
D
∩
D
≠
∅
}

gD \cap D \ne \emptyset \}

. In this paper the recursive structure for the growth function of

(
G
,
Σ
)

(G,\Sigma )

is computed, and it is proved that the growth function

f
f

is reciprocal

(
f
(
z
)
=
f
(
1

/

z
)
)

(f(z) = f(1/z))

except for some exceptional cases when

D
D

has three, four, or five sides.
Unipotent representations and reductive dual pairs over finite fields
Authors: Adams Jeffrey , Moy Allen
Published: June 2012

Consider the representation correspondence for a reductive dual pair

(

G
1

,

G
2

)

({G_1},{G_2})

over a finite field. We consider the question of how the correspondence behaves for unipotent representations. In the special case of cuspidal unipotent representations, and a certain fundamental situation, that of "first occurrence", the representation correspondence takes a cuspidal unipotent representation of

G
1

{G_1}

to one of

G
2

{G_2}

. This should serve as a fundamental case in studying the correspondence in general over both finite and local fields.
Fibered products of homogeneous continua
Authors: Villarreal Karen
Published: June 2012

In this paper, we construct homogeneous continua by using a fibered product of a homogeneous continuum

X
X

with itself. The space

X
X

must have a continuous decomposition into continua, and it must possess a certain type of homogeneity property with respect to this decomposition. It is known that the points of any one-dimensional, homogeneous continuum can be "blown up" into pseudo-arcs to form a new continuum with a continuous decomposition into pseudo-arcs. We will show that these continua can be used in the above construction. Finally, we will show that the continuum constructed by using the pseudo-arcs, the circle of pseudo-arcs, or the solenoid of pseudo-arcs is not homeomorphic to any known homogeneous continuum.
Gauss map of minimal surfaces with ramification
Authors: Ru Min
Published: June 2012

We prove that for any complete minimal surface

M
M

immersed in

R
n

{R^n}

, if in

C

P

n
−
1

C{P^{n - 1}}

there are

q
>
n
(
n
+
1
)

/

2

q > n(n + 1)/2

hyperplanes

H
j

{H_j}

in general position such that the Gauss map of

M
M

is ramified over

H
j

{H_j}

with multiplicity at least

e
j

{e_j}

for each

j
j

and
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="sigma-summation Underscript j equals 1 Overscript q Endscripts left-parenthesis 1 minus StartFraction left-parenthesis n minus 1 right-parenthesis Over e Subscript j Baseline EndFraction right-parenthesis greater-than n left-parenthesis n plus 1 right-parenthesis slash 2">

∑

j
=
1

q

(

1
−

(
n
−
1
)

e
j

)

>
n
(
n
+
1
)

/

2

\sum \limits _{j = 1}^q {\left ({1 - \frac {{(n - 1)}} {{{e_j}}}} \right ) > n(n + 1)/2}

\]
, then

M
M

must be flat.
Division algebra coproducts of index 𝑛
Authors: Van den Bergh Michel , Schofield Aidan
Published: June 2012

Given a family of separable finite dimensional extensions

{

L
i

}

\{ {L_i}\}

of a field

k
k

, we construct a division algebra

n
2

{n^2}

over its center which is freely generated over

k
k

by the fields

{

L
i

}

\{ {L_i}\}

.
A singular representation of 𝐸₆
Authors: Binegar B. , Zierau R.
Published: June 2012

Algebraic properties of a singular representation of

E

6

{{\mathbf {E}}_6}

are studied. This representation has the Joseph ideal as its annihilator and it remains irreducible when restricted to

F

4

{{\mathbf {F}}_4}

.
Projective resolutions and Poincaré duality complexes
Authors: Benson D. J. , Carlson Jon F.
Published: June 2012

Let k be a field lof characteristic

p
>
0

p > 0

and let G be a finite group. We investigate the structure of the cohomology ring

H
∗

(
G
,
k
)

{H^\ast }(G,k)

in relation to certain spectral sequences determined by systems of homogeneous parameters for the cohomology ring. Each system of homogeneous parameters is associated to a complex of projective kG-modules which is homotopically equivalent to a Poincaré duality complex. The initial differentials in the hypercohomology spectral sequence of the complex are multiplications by the parameters, while the higher differentials are matric Massey products. If the cohomology ring is Cohen-Macaulay, then the duality of the complex assures that the Poincaré series for the cohomology satisfies a certain functional equation. The structure of the complex also implies the existence of cohomology classes which are in relatively large degrees but are not in the ideal generated by the parameters. We consider several other questions concerned with the minimal projective resolutions and the convergence of the spectral sequence.
On transformation group 𝐶*-algebras with continuous trace
Authors: Echterhoff Siegfried
Published: June 2012

In this paper we answer some questions posed by Dana Williams in [19] concerning the problem under which conditions the transformation group

C
∗

{C^ \ast }

-algebra

C
∗

(
G
,
Ω
)

{C^\ast }(G,\Omega )

of a locally compact transformation group (G,

Ω
\Omega

) has continuous trace. One consequence will be, for compact G, that

C
∗

(
G
,
Ω
)

{C^\ast }(G,\Omega )

has continuous trace if and only if the stabilizer map is continuous. We also give a complete solution to the problem if G is discrete.
Nonlinear stability of rarefaction waves for a viscoelastic material with memory
Authors: Hattori Harumi
Published: June 2012

In this paper we will discuss the stability of rarefaction waves for a viscoelastic material with memory. The rarefaction waves for which the stability is tested are not themselves solutions to the integrodifferential equations (1.1) governing the viscoelastic material. They are solutions to a related equilibrium system of conservation laws given by (1.11). We shall show that if the forcing term and the past history are small and if the initial data are close to the rarefaction waves, the solutions to (1.1) will approach the rarefaction waves in sup norm as the time goes to infinity.
On the Gorenstein property of Rees and form rings of powers of ideals
Authors: Herrmann M. , Ribbe J. , Zarzuela S.
Published: June 2012

In this paper we determine the exponents n for which the Rees ring

R
(

I
n

)

R({I^n})

and the form ring

gr

A

(

I
n

)

{\text {gr}}_{A}({I^n})

are Gorenstein rings, where I is a strongly Cohen-Macaulay ideal of linear type (including complete and almost complete intersections) or an

m

\mathfrak {m}

-primary ideal in a local ring A with maximal ideal

m

\mathfrak {m}

.
An almost strongly minimal non-Desarguesian projective plane
Authors: Baldwin John T.
Published: June 2012

There is an almost strongly minimal projective plane which is not Desarguesian.
Multivariate orthogonal polynomials and operator theory
Authors: Xu Yuan
Published: June 2012

The multivariate orthogonal polynomials are related to a family of commuting selfadjoint operators. The spectral theorem for these operators is used to prove that a polynomial sequence satisfying a vector-matrix form of the three-term relation is orthonormal with a determinate measure.
Gromov’s compactness theorem for pseudo holomorphic curves
Authors: Ye Rugang
Published: June 2012

We give a complete proof for Gromov’s compactness theorem for pseudo holomorphic curves both in the case of closed curves and curves with boundary.
Amenability and the structure of the algebras 𝐴_{𝑝}(𝐺)
Authors: Forrest Brian
Published: June 2012

A number of characterizations are given of the class of amenable locally compact groups in terms of the ideal structure of the algebras

A
p

(
G
)

{A_p}(G)

. An almost connected group is amenable if and only if for some

1
>
p
>
∞

1 > p > \infty

and some closed ideal I of

A
p

(
G
)

{A_p}(G)

, I has a bounded approximate identity. Furthermore, G is amenable if and only if every derivation of

A
p

(
G
)

{A_p}(G)

into a Banach

A
p

(
G
)

{A_p}(G)

-bimodule is continuous.
Eigenvalues and eigenspaces for the twisted Dirac operator over 𝑆𝑈(𝑁,1) and 𝑆𝑝𝑖𝑛(2𝑁,1)
Authors: Galina Esther , Vargas Jorge
Published: June 2012

Let X be a symmetric space of noncompact type whose isometry group is either

S
U
(
n
,
1
)

SU(n,1)

or

S
p
i
n
(
2
n
,
1
)

Spin(2n,1)

. Then the Dirac operator D is defined on

L
2

{L^2}

-sections of certain homogeneous vector bundles over X. Using representation theory we obtain explicitly the eigenvalues of D and describe the eigenspaces in terms of the discrete series.
Hodge decompositions and Dolbeault complexes on normal surfaces
Authors: Fox Jeffrey , Haskell Peter
Published: June 2012

Give the smooth subset of a normal singular complex projective surface the metric induced from the ambient projective space. The

L
2

{L^2}

cohomology of this incomplete manifold is isomorphic to the surface’s intersection cohomology, which has a natural Hodge decomposition. This paper identifies Dolbeault complexes whose

∂
¯

\bar \partial

-closed and

∂
¯

\bar \partial

-coclosed forms represent the classes of pure type in the corresponding Hodge decomposition of

L
2

{L^2}

cohomology.
The orders of solutions of the Kummer system of congruences
Authors: Skula Ladislav
Published: June 2012

A new method concerning solutions of the Kummer system of congruences (K) (modulo an odd prime l) is developed. This method is based on the notion of the Stickelberger ideal. By means of this method a new proof of Pollaczek’s and Morishima’s assertion on solutions of (K) of orders 3, 6 and 4

mod

l

\bmod \; l

is given. It is also shown that in case there is a solution of

(
K
)

≢

0
,
±
1

(
mod

l
)

(K)\, \not \equiv \, 0, \pm 1\;\pmod l

, then for the index of irregularity

i
(
l
)

i(l)

of the prime l we have

i
(
l
)
≥
[

l

/

2

3

]

i(l) \geq [\sqrt [3]{{l/2}}]

.
Generalized Casson invariants for 𝑆𝑂(3),𝑈(2),𝑆𝑝𝑖𝑛(4), and 𝑆𝑂(4)
Authors: Curtis Cynthia L.
Published: June 2012

We investigate Casson-type invariants corresponding to the low-rank groups

SO

(
3
)

{\text {SO}}(3)

,

SU

(
2
)
×

S
1

{\text {SU}}(2) \times {S^1}

,

U

(
2
)

{\text {U}}(2)

,

Spin

(
4
)

{\text {Spin}}(4)

and

SO

(
4
)

{\text {SO}}(4)

. The invariants are defined following an approach similar to those of K. Walker and S. Cappell, R. Lee, and E. Miller. We obtain a description for each of the invariants in terms of the

SU

(
2
)

{\text {SU}}(2)

-invariant. Thus, all of them may be calculated using formulae for the

SU

(
2
)

{\text {SU}}(2)

-invariant. In defining these invariants, we offer methods which should prove useful for studying the invariants for other non-simply-connected groups once the invariants for the simply-connected covering groups are known.
Decompositions for relatively normal lattices
Authors: Hart James B. , Tsinakis Constantine
Published: June 2012

Continuing the work begun in Snodgrass and Tsinakis [26, 27], we develop a family of decomposition theorems for classes of relatively normal lattices. These results subsume and are inspired by known decomposition theorems in order-algebra due to P. Conrad and D. B. McAlister. As direct corollaries of the main results, we obtain corresponding decomposition theorems for classes of partially ordered sets.
Approximate solutions to first and second order quasilinear evolution equations via nonlinear viscosity
Authors: Esteban Juan R. , Marcati Pierangelo
Published: June 2012

We shall consider a model problem for the fully nonlinear parabolic equation\[ut+F(x,t,u,Du,εD2u)=0{u_t} + F(x,t,u,Du,\varepsilon {D^2}u) = 0\]and we study both the approximating degenerate second order problem and the related first order equation, obtained by the limit asε→0\varepsilon \to 0. The strong convergence of the gradients is provided by semiconcavity unilateral bounds and by the supremum bounds of the gradients. In this way we find solutions in the class of viscosity solutions of Crandall and Lions.
Representable 𝐾-theory of smooth crossed products by 𝑅 and 𝑍
Authors: Phillips N. Christopher , Schweitzer Larry B.
Published: June 2012

We show that the Thorn isomorphism and the Pimsner-Voiculescu exact sequence both hold for smooth crossed products of Fréchet algebras by

R

\mathbb {R}

and

Z

\mathbb {Z}

respectively. We also obtain the same results for

L
1

{L^1}

-crossed products of Banach algebras by

R

\mathbb {R}

and

Z

\mathbb {Z}

.
Rational homotopy of the space of self-maps of complexes with finitely many homotopy groups
Authors: Smith Samuel B.
Published: June 2012

For simply connected CW complexes X with finitely many, finitely generated homotopy groups,

1

^{1}

the path components of the function space

M
(
X
,
X
)

M(X,X)

of free self-maps of X are all of the same rational homotopy type if and only if all the k-invariants of X are of finite order. In case X is rationally a two-stage Postnikov system the space

M
0

(
X
,
X
)

{M_0}(X,X)

of inessential self-maps of X has the structure of rational H-space if and only if the k-invariants of X are of finite order.
Müntz systems and orthogonal Müntz-Legendre polynomials
Authors: Borwein Peter , Erdélyi Tamás , Zhang John
Published: June 2012

The Müntz-Legendre polynomials arise by orthogonalizing the Müntz system

{

x

λ
0

,

x

λ
1

,
…
}

\{ {x^{{\lambda _0}}},{x^{{\lambda _1}}}, \ldots \}

with respect to Lebesgue measure on [0, 1]. In this paper, differential and integral recurrence formulae for the Müntz-Legendre polynomials are obtained. Interlacing and lexicographical properties of their zeros are studied, and the smallest and largest zeros are universally estimated via the zeros of Laguerre polynomials. The uniform convergence of the Christoffel functions is proved equivalent to the nondenseness of the Müntz space on [0, 1], which implies that in this case the orthogonal Müntz-Legendre polynomials tend to 0 uniformly on closed subintervals of [0, 1). Some inequalities for Müntz polynomials are also investigated, most notably, a sharp

L
2

{L^2}

Markov inequality is proved.
Mean value inequalities in Hilbert space
Authors: Clarke F. H. , Ledyaev Yu. S.
Published: June 2012

We establish a new mean value theorem applicable to lower semi-continuous functions on Hilbert space. A novel feature of the result is its "multidirectionality": it compares the value of a function at a point to its values on a set. We then discuss some refinements and consequences of the theorem, including applications to calculus, flow invariance, and generalized solutions to partial differential equations. Résumé. On établit un nouveau théorème de la valeur moyenne qui s’applique aux fonctions semicontinues inférieurement sur un espace de Hilbert. On déduit plusieurs conséquences du résultat portant, par exemple, sur les fonctions monotones et sur les solutions généralisées des équations aux dérivées partielles.
Periodic orbits for Hamiltonian systems in cotangent bundles
Authors: Golé Christophe
Published: June 2012

We prove the existence of at least

cl
⁡
(
M
)

\operatorname {cl}(M)

periodic orbits for certain time-dependent Hamiltonian systems on the cotangent bundle of an arbitrary compact manifold M. These Hamiltonians are not necessarily convex but they satisfy a certain boundary condition given by a Riemannian metric on M. We discretize the variational problem by decomposing the time-1 map into a product of "symplectic twist maps". A second theorem deals with homotopically non-trivial orbits of negative curvature.
Fractal properties of invariant subsets for piecewise monotonic maps on the interval
Authors: Hofbauer Franz , Urbański Mariusz
Published: June 2012

Let T be a piecewise monotonic transformation on [0, 1] and let A be a T-invariant subset, which has positive topological entropy and satisfies the Darboux property. A general existence theorem for conformal measures on A is proved. This is then used to show equality of the dynamical dimension of A and the minimal zero of a certain pressure function.
A general view of reflexivity
Authors: Hadwin Don
Published: June 2012

Various concepts of reflexivity for an algebra or linear space of operators have been studied by operator theorists and algebraists. This paper contains a very general version of reflexivity based on dual pairs of vector spaces over a Hausdorff field. The special cases include topological, algebraic and approximate reflexivity. In addition general versions of hyperreflexivity and direct integrals are introduced. We prove general versions of many known (and some new) theorems, often with simpler proofs.
A 4-dimensional Kleinian group
Authors: Bowditch B. H. , Mess G.
Published: June 2012

We give an example of a 4-dimensional Kleinian group which is finitely generated but not finitely presented, and is a subgroup of a cocompact Kleinian group.
Spectral analysis for the generalized Hermite polynomials
Authors: Krall Allan M.
Published: June 2012

The operator theory associated with the Hermite polynomials does not extend to the generalized Hermite polynomials because the even and odd polynomials satisfy different differential equations. We show that this leads to two problems, each of interest on its own. We then weld them together to form a united spectral expansion. In addition, the exponent

μ
\mu

in the weight

|

x

|

2
μ

e

−

x
2

|x{|^{2\mu }}{e^{ - {x^2}}}

has traditionally always been greater than

−

1
2

- \frac {1}{2}

. We show what happens if

μ
≤
−

1
2

\mu \leq - \frac {1}{2}

. Finally, we examine the differential equations in left-definite spaces.
On the core of a cone-preserving map
Authors: Tam Bit Shun , Schneider Hans
Published: June 2012

This is the third of a sequence of papers in an attempt to study the Perron-Frobenius theory of a nonnegative matrix and its generalizations from the cone-theoretic viewpoint. Our main object of interest here is the core of a cone-preserving map. If A is an

n
×
n

n \times n

real matrix which leaves invariant a proper cone K in

R

n

{\mathbb {R}^n}

, then by the core of A relative to K, denoted by

core

K

(
A
)

{\text {core}}_K(A)

, we mean the convex cone

⋂

i
=
1

∞

A
i

K

\bigcap \nolimits _{i = 1}^\infty {{A^i}K}

. It is shown that when

core

K

(
A
)

{\text {core}}_K(A)

is polyhedral, which is the case whenever K is, then

core

K

(
A
)

{\text {core}}_K(A)

is generated by the distinguished eigenvectors of positive powers of A. The important concept of a distinguished A-invariant face is introduced, which corresponds to the concept of a distinguished class in the nonnegative matrix case. We prove a significant theorem which describes a one-to-one correspondence between the distinguished A-invariant faces of K and the cycles of the permutation induced by A on the extreme rays of

core

K

(
A
)

{\text {core}}_K(A)

, provided that the latter cone is nonzero, simplicial. By an interplay between cone-theoretic and graph-theoretic ideas, the extreme rays of the core of a nonnegative matrix are fully described. Characterizations of K-irreducibility or A-primitivity of A are also found in terms of

core

K

(
A
)

{\text {core}}_K(A)

. Several equivalent conditions are also given on a matrix with an invariant proper cone so that its spectral radius is an eigenvalue of index one. An equivalent condition in terms of the peripheral spectrum is also found on a real matrix A with the Perron-Schaefer condition for which there exists a proper invariant cone K suchthat

core

K

(
A
)

{\text {core}}_K(A)

is polyhedral, simplicial, or a single ray. A method of producing a large class of invariant proper cones for a matrix with the Perron-Schaefer condition is also offered.
A Banach space not containing 𝑐₀,𝑙₁ or a reflexive subspace
Authors: Gowers W. T.
Published: June 2012

An infinite-dimensional Banach space is constructed which does not contain

c
0

{c_0}

,

l
1

{l_1}

or an infinite-dimensional reflexive subspace. In fact, it does not even contain

l
1

{l_1}

or an infinite-dimensional subspace with a separable dual.
Kinematic formulas for mean curvature powers of hypersurfaces and Hadwiger’s theorem in 𝑅²ⁿ
Authors: Zhou Jia Zu
Published: June 2012

We first discuss the theory of hypersurfaces and submanifolds in the m-dimensional Euclidean space leading up to high dimensional analogues of the classical Euler’s and Meusnier’s theorems. Then we deduce the kinematic formulas for powers of mean curvature of the

(
m
−
2
)

(m - 2)

-dimensional intersection submanifold

S
0

∩
g

S
1

{S_0} \cap g{S_1}

of two

C
2

{C^2}

-smooth hypersurfaces

S
0

{S_0}

,

S
1

{S_1}

, i.e.,

∫
G

(

∫

S
0

∩
g

S
1

H

2
k

d
σ
)
d
g

{\smallint _G}({\smallint _{{S_0} \cap g{S_1}}}{H^{2k}}d\sigma )dg

. Many well-known results, for example, the C-S. Chen kinematic formula and Crofton type formulas are easy consequences of our kinematic formulas. As direct applications of our formulas, we obtain analogues of Hadwiger’s theorem in

R

2
n

{\mathbb {R}^{2n}}

, i.e., sufficient conditions for one domain

K
β

{K_\beta }

to contain, or to be contained in, another domain

K
α

{K_\alpha }

.
Optimal drift on [0,1]
Authors: Lee Susan
Published: June 2012

Consider one-dimensional diffusions on the interval

[
0
,
1
]

[0,1]

of the form

d

X
t

=
d

B
t

+
b
(

X
t

)
d
t

d{X_t} = d{B_t} + b({X_t})dt

, with

0
0

a reflecting boundary,

b
(
x
)
⩾
0

b(x) \geqslant 0

, and

∫
0
1

b
(
x
)
d
x
=
1

\int _0^1 {b(x)dx = 1}

. In this paper, we show that there is a unique drift which minimizes the expected time for

X
t

{X_t}

to hit

1
1

, starting from

X
0

=
0

{X_0} = 0

. In the deterministic case

d

X
t

=
b
(

X
t

)
d
t

d{X_t} = b({X_t})dt

, the optimal drift is the function which is identically equal to

1
1

. By contrast, if

d

X
t

=
d

B
t

+
b
(

X
t

)
d
t

d{X_t} = d{B_t} + b({X_t})dt

, then the optimal drift is the step function which is

2
2

on the interval

[
1

/

4
,
3

/

4
]

[1/4,3/4]

and is

0
0

otherwise. We also solve this problem for arbitrary starting point

X
0

=

x
0

{X_0} = {x_0}

and find that the unique optimal drift depends on the starting point,

x
0

{x_0}

, in a curious manner.
Block Jacobi matrices and zeros of multivariate orthogonal polynomials
Authors: Xu Yuan
Published: June 2012

A commuting family of symmetric matrices are called the block Jacobi matrices, if they are block tridiagonal. They are related to multivariate orthogonal polynomials. We study their eigenvalues and joint eigenvectors. The joint eigenvalues of the truncated block Jacobi matrices correspond to the common zeros of the multivariate orthogonal polynomials.
𝐿^{𝑝}-boundedness of pseudo-differential operators of class 𝑆_{0,0}
Authors: Hwang I. L. , Lee R. B.
Published: June 2012

We study the

L
p

{L^p}

-boundedness of pseudo-differential operators with the support of their symbols being contained in

E
×

R

n

E \times {{\mathbf {R}}^n}

, where

E
E

is a compact subset of

R

n

{{\mathbf {R}}^n}

, and their symbols have derivatives with respect to

x
x

only up to order

k
k

, in the Hölder continuous sense, where

k
>
n

/

2

k > n/2

(the case

1
>
p
⩽
2

1 > p \leqslant 2

) and

k
>
n

/

p

k > n/p

(the case

2
>
p
>
∞

2 > p > \infty

). We also give a new proof of the

L
p

{L^p}

-boundedness,

1
>
p
>
∞

1 > p > \infty

, of pseudo-differential operators of class

S

0
,
0

m

S_{0,0}^m

, where

m
=
m
(
p
)
=
−
n

|

1

/

p
−
1

/

2

|

m = m(p) = - n|1/p - 1/2|

, and

a
∈

S

0
,
0

m

a \in S_{0,0}^m

satisfies
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartAbsoluteValue partial-differential Subscript x Superscript alpha Baseline partial-differential Subscript xi Superscript beta Baseline a left-parenthesis x comma xi right-parenthesis EndAbsoluteValue less-than-or-slanted-equals upper C Subscript alpha comma beta Baseline mathematical left-angle xi mathematical right-angle Superscript m">

|

∂
x
α

∂
ξ
β

a
(
x
,
ξ
)

|

⩽

C

α
,
β

⟨
ξ

⟩
m

|\partial _x^\alpha \partial _\xi ^\beta a(x,\xi )| \leqslant {C_{\alpha ,\beta }}{\langle \xi \rangle ^m}

for

(
x
,
ξ
)
∈

R

n

×

R

n

,

|

α

|

⩽
k

(x,\xi ) \in {{\mathbf {R}}^n} \times {{\mathbf {R}}^n},|\alpha | \leqslant k

and

|

β

|

⩽

k
′

|\beta | \leqslant k’

, in the Hölder continuous sense, where

k
>
n

/

2
,

k
′

>
n

/

p

k > n/2,k’ > n/p

(the case

1
>
p
⩽
2

1 > p \leqslant 2

) and

k
>
n

/

p
,

k
′

>
n

/

2

k > n/p,k’ > n/2

(the case

2
>
p
>
∞

2 > p > \infty

).
A family of real 2ⁿ-tic fields
Authors: Shen Yuan Yuan , Washington Lawrence C.
Published: June 2012

We study the family of polynomials
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper P Subscript n Baseline left-parenthesis upper X semicolon a right-parenthesis equals normal fraktur upper R left-parenthesis left-parenthesis upper X plus i right-parenthesis Superscript 2 Super Superscript n Superscript Baseline right-parenthesis minus StartFraction a Over 2 Superscript n Baseline EndFraction normal fraktur upper I left-parenthesis left-parenthesis upper X plus i right-parenthesis Superscript 2 Super Superscript n Superscript Baseline right-parenthesis">

P
n

(
X
;
a
)
=
ℜ
(

(
X
+
i

)

2
n

)
−

a

2
n

ℑ
(

(
X
+
i

)

2
n

)

{P_n}(X;a) = \Re ({(X + i)^{{2^n}}}) - \frac {a}{{{2^n}}}\Im ({(X + i)^{{2^n}}})

\]
and determine when

P
n

(
X
;
a
)

{P_n}(X;a)

,

a
∈

Z

a \in \mathbb {Z}

, is irreducible. The roots are all real and are permuted cyclically by a linear fractional transformation defined over the real subfield of the

2
n

{2^n}

th cyclotomic field. The families of fields we obtain are natural extensions of those studied by M.-N. Gras and Y.-Y. Shen, but in general the present fields are non-Galois for

n
≥
4

n \geq 4

. From the roots we obtain a set of independent units for the Galois closure that generate an "almost fundamental piece" of the full group of units. Finally, we discuss the two examples where our fields are Galois, namely

a
=
±

2
n

a = \pm {2^n}

and

a
=
±

2
4

∙
239

a = \pm {2^4} \bullet 239

.
Global oscillatory waves for second order quasilinear wave equations
Authors: Godin Paul
Published: June 2012

In this paper we prove the global existence and describe the asymptotic behaviour of a family of oscillatory solutions of Cauchy problems for a class of scalar second order quasilinear wave equations, when the space dimension is odd and at least equal to

3
3

. If time is bounded, corresponding results for quasilinear first order systems were obtained by Guès; to prove our results we reduce our problems to bounded time problems with the help of a conformal inversion. To obtain global results, suitable geometric assumptions must be made on the set where the oscillations are concentrated at initial time.
Conical limit points and groups of divergence type
Authors: Hong Sungbok
Published: June 2012

We use the Patterson-Sullivan measure to generalize Agard’s theorem to all groups of divergence type. As a consequence, we prove that for a nonelementary group

Γ
\Gamma

of divergence type, the conical limit set has positive Patterson-Sullivan measure.
BMO on strongly pseudoconvex domains: Hankel operators, duality and \overline∂-estimates
Authors: Li Huiping , Luecking Daniel H.
Published: June 2012

We study the condition that characterizes the symbols of bounded Hankel operators on the Bergman space of a strongly pseudoconvex domain and show that it is equivalent to

B
M
O

BMO

plus analytic. (Here we mean the Bergman metric

B
M
O

BMO

of Berger, Coburn and Zhu.) In the course of the proof we obtain new

∂
¯

\overline \partial

-estimates that may be of independent interest. Some applications include a decomposition of

B
M
O

BMO

similar to the classical

L
∞

+

L
∞

~

{L^\infty } + \widetilde {{L^\infty }}

, and two characterizations of the dual of

V
M
O

VMO

(which is also a predual of

B
M
O

BMO

). In addition, we obtain some partial results on the boundedness of Hankel operators in

L
1

{L^1}

norm.
Modular Schur functions
Authors: Walker Grant
Published: June 2012

A new family of symmetric functions is considered. These functions are analogous to the classical Schur functions, but depend on an integer modulus

p
⩾
2

p \geqslant 2

, as well as on a partition

λ
\lambda

. In the case where

p
p

is prime, certain of these functions are shown to be irreducible characters of the general linear group

G
L
(
n
,
K
)

GL(n,K)

in the natural characteristic

p
p

of the field

K
K

. This dualises a wellknown criterion of G. D. James for such characters to be given by classical Schur functions.
On square-preserving isometries of convolution algebras
Authors: Saeki Sadahiro
Published: June 2012

Let

S
S

and

S
′

S’

be two semigroups, each contained in a locally compact group. Under certain conditions on

S
S

and

S
′

S’

, we shall characterize those isometric additive surjections

T
:
M
(
S
)
→
M
(

S
′

)

T:M(S) \to M(S’)

which preserve convolution squares. Our results generalize the classical results of Wendel and of Johnson and also Patterson’s characterization of isometric involutions on measure algebras.
Further results on fixpoints and zeros of entire functions
Authors: Zheng Jian Hua , Yang Chung-Chun
Published: June 2012

In this paper, a quantitative estimation on the number of zeros of the function

f
∘
g
(
z
)
−
α
(
z
)

f \circ g(z) - \alpha (z)

is derived, where

f
f

and

g
g

are transcendental entire functions and

α
(
z
)

\alpha (z)

a nonconstant polynomial. As an application of this and a further step towards an affirmative answer to a conjecture of Baker, a quantitative estimation on the number of period points of exact order

n
n

of

f
n

{f_n}

(

n
n

th iterate of

f
f

) is obtained.
Prime ideals in polynomial rings over one-dimensional domains
Authors: Heinzer William , Wiegand Sylvia
Published: June 2012

Let

R
R

be a one-dimensional integral domain with only finitely many maximal ideals and let

x
x

be an indeterminate over

R
R

. We study the prime spectrum of the polynomial ring

R
[
x
]

R[x]

as a partially ordered set. In the case where

R
R

is countable we classify

Spec
⁡
(
R
[
x
]
)

\operatorname {Spec} (R[x])

in terms of splitting properties of the maximal ideals

m

{\mathbf {m}}

of

R
R

and the valuative dimension of

R

m

{R_{\mathbf {m}}}_{}

.
On the number of solutions of a third-order boundary value problem
Authors: Rovderová Eva
Published: June 2012

This paper deals with the number of solutions of the third-order boundary value problem

y
′

=
f
(
t
,
y
,

y
′

,
y
)

y’ = f(t,y,y’,y)

,

y
(
0
)
=

A
0

y(0) = {A_0}

,

y
′

(
0
)
=

A
1

y’(0) = {A_1}

,

y
(
T
)
=
B

y(T) = B

. This number of solutions is investigated in connection with the number of zeros of a solution for the corresponding variational problem.
On closed minimal submanifolds in pinched Riemannian manifolds
Authors: Xu Hong Wei
Published: June 2012

In this paper, we first prove a generalized Simons integral inequality for closed minimal submanifolds in a Riemannian manifold. Second, we prove a pinching theorem for closed minimal submanifolds in a complete simply connected pinched Riemannian manifold, which generalizes the results obtained by S. S. Chern, M. do Carmo, and S. Kobayashi and A. M. Li and J. M. Li respectively. Finally, we obtain a distribution theorem for the square norm of the second fundamental form of

M
M

under the assumption that

M
M

is a minimal submanifold with parallel second fundamental form in a Riemannian manifold.
Convexity of the ideal boundary for complete open surfaces
Authors: Yim Jin-Whan
Published: June 2012

For complete open surfaces admitting total curvature, we define several kinds of convexity for the ideal boundary, and provide examples of each of them. We also prove that a surface with most strongly convex ideal boundary is in fact a generalization of a Hadamard manifold in the sense that the ideal boundary consists entirely of Busemann functions.
Cauchy-Green type formulae in Clifford analysis
Authors: Ryan John
Published: June 2012

A Cauchy integral formula is constructed for solutions to the polynomial Dirac equation(Dk+∑m=0k−1bmDm)f=0({D^k} + \sum \nolimits _{m = 0}^{k - 1} {{b_m}{D^m})f = 0}, where eachbm{b_m}is a complex number,DDis the Dirac operator inRn{R^n}, andffis defined on a domain inRn^{{R^n}}and takes values in a complex Clifford algebra. Some basic properties for the solutions to this equation, arising from the integral formula, are described, including an approximation theorem. We also introduce a Bergman kernel for square integrable solutions to(D+λ)f=0(D + \lambda )f = 0over bounded domains with piecewiseC1{C^1}, or Lipschitz, boundary.
Some recurrence formulas for spherical polynomials on tube domains
Authors: Zhang Gen Kai
Published: June 2012

For a tube domain

G

/

K

G/K

we study the tensor products of two spherical representations of the maximal compact group

K
K

and the product of the corresponding spherical polynomials. When one of these is a fundamental representation, we prove that the spherical representations appear with multiplicity at most one and we then find all the coefficients in the recurrence formula for the product of the spherical polynomials. This generalizes the previous result of L. Vretare and proves for certain cases a conjecture of R. Stanley on Jack symmetric polynomials.
On the 𝐿² inequalities involving trigonometric polynomials and their derivatives
Authors: Chen Weiyu
Published: June 2012

In this note we study the upper bound of the integral
\[

∫
0
π

(

t

(
k
)

(
x
)
)

2

w
(
x
)

d
x

\int _0^\pi {{{({t^{(k)}}(x))}^2}w(x)} dx

\]
where

t
(
x
)

t(x)

is a trigonometric polynomial with real coefficients such that

‖
t
‖

∞
⩽
1

\left \| t \right \|\infty \leqslant 1

and

w
(
x
)

w(x)

is a nonnegative function defined on

[
0
,
π
]

[0,\pi ]

. When

w
(
x
)
=

sin
j

⁡
x

w(x) = \sin ^jx

, where

j
j

is a positive integer, we obtain the exact upper bound for the above integral.
Random quadratic forms
Authors: Gregory John , Hughes H. R.
Published: June 2012

The results of Boyce for random Sturm-Liouville problems are generalized to random quadratic forms. Order relationships are proved between the means of eigenvalues of a random quadratic form and the eigenvalues of an associated mean quadratic form. Finite-dimensional and infinite-dimensional examples that show these are the best possible results are given. Also included are some results for a general approximation theory for random quadratic forms.
A convergence theorem for Riemannian submanifolds
Authors: Shen Zhong Min
Published: June 2012

In this paper we study the convergence of Riemannian submanifolds. In particular, we prove that any sequence of closed submanifolds with bounded normal curvature and volume in a closed Riemannian manifold subconverge to a closed submanifold in the

C

1
,
α

{C^{1,\alpha }}

topology. We also obtain some applications to irreducible homogeneous manifolds and pseudo-holomorphic curves in symplectic manifolds.
A norm convergence result on random products of relaxed projections in Hilbert space
Authors: Bauschke H. H.
Published: June 2012

Suppose

X
X

is a Hilbert space and

C
1

,
…
,

C
N

{C_1}, \ldots ,{C_N}

are closed convex intersecting subsets with projections

P
1

,
…
,

P
N

{P_1}, \ldots ,{P_N}

. Suppose further

r
r

is a mapping from

N

\mathbb {N}

onto

{
1
,
…
,
N
}

\{ 1, \ldots ,N\}

that assumes every value infinitely often. We prove (a more general version of) the following result: If the

N
N

-tuple

(

C
1

,
…
,

C
N

)

({C_1}, \ldots ,{C_N})

is "innately boundedly regular", then the sequence

(

x
n

)

({x_n})

, defined by
\[

x
0

∈
X

arbitrary,

x

n
+
1

:=

P

r
(
n
)

x
n

,

for all

n
⩾
0
,

{x_0} \in X\;{\text {arbitrary,}}\quad {x_{n + 1}}: = {P_{r(n)}}{x_n},\quad {\text {for all}}\;n \geqslant 0,

\]
converges in norm to some point in

∩

i
=
1

N

C
i

\cap _{i = 1}^N{C_i}

. Examples without the usual assumptions on compactness are given. Methods of this type have been used in areas like computerized tomography and signal processing.
Simultaneous triangularizability, near commutativity and Rota’s theorem
Authors: Jafarian A. A. , Radjavi H. , Rosenthal P. , Sourour A. R.
Published: June 2012

In this paper we consider simultaneously triangularizable collections of compact operators and show that similarities of any finite subcollection can be made arbitrarily close to commuting normal operators. As a consequence, we obtain a variant of a theorem of G.-C. Rota. Also, we give some sufficient conditions for simultaneous triangularization of collections of compact operators. Finally, several counterexamples are given.