bluuebunny/crossref_metadata_2025 huggingface dataset:
von Neumann’s inequality for commuting, diagonalizable contractions. I
Authors: Lotto B. A.
Published: June 2010

We obtain a sufficient condition for an

n
n

-tuple

T
T

of commuting, diagonalizable contractions on a finite-dimensional space to satisfy von Neumann’s inequality
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartAbsoluteValue EndAbsoluteValue p left-parenthesis upper T right-parenthesis StartAbsoluteValue EndAbsoluteValue less-than-or-slanted-equals StartAbsoluteValue EndAbsoluteValue p StartAbsoluteValue EndAbsoluteValue Subscript normal infinity">

|

|

p
(
T
)

|

|

⩽

|

|

p

|

|

∞

||p(T)|| \leqslant ||p|{|_\infty }

for any polynomial

p
p

in

n
n

variables, where

|

|

p

|

|

∞

||p|{|_\infty }

denotes the supremum of

|

p

|

|p|

over the unit polydisk in

C

n

{{\mathbf {C}}^n}

. We apply this condition to the case where

T
T

acts on a two- or three-dimensional space. In addition, we prove that von Neumann’s inequality for commuting, diagonalizable contractions on a three-dimensional space implies von Neumann’s inequality for arbitrary commuting contractions on a three-dimensional space.
An index formula for 𝑛-tuple of shifts on polydisk
Authors: Yan Ke Ren
Published: June 2010

Let

(

M

z
1

,
…
,

M

z
n

)

({M_{{z_1}}}, \ldots ,{M_{{z_n}}})

be an n-tuple of shift operators on the polydisk

l
2

(

Z

n

)

{l^2}({{\mathbf {Z}}^n})

; we compress it to a variety of subspaces of

l
2

(

Z

n

)

{l^2}({{\mathbf {Z}}^n})

that are combinatorially constructed. The main result is a multivariate Fredholm index formula, which links the indices of the n-tuples to their combinatorial data in the definitions of the subspaces.
Locally finite and locally nilpotent derivations with applications to polynomial flows, morphisms and 𝒢ₐ-actions. II
Authors: van den Essen Arno
Published: June 2010

This paper describes several applications of locally finite and locally nilpotent derivations; we recover the main results from the theory of polynomial flows, give a new inversion formula for polynomial automorphisms, reformulate the Eulerian conjecture for ordinary systems of differential equations in terms of locally nilpotent derivations, and give an algorithm to compute the invariant ring of a

G

a

{\mathcal {G}_a}

-action on affine n-space (if this ring is finitely generated).
Torsion units in integral group rings
Authors: Valenti Angela
Published: June 2010

Let

G
=

⟨
a
⟩

⋊
X

G = \left \langle a \right \rangle \rtimes X

where

⟨
a
⟩

\left \langle a \right \rangle

is a cyclic group of order

n
,
X

n,X

is an abelian group of order

m
m

, and

(
n
,
m
)
=
1

(n,m) = 1

. We prove that if

Z

G

\mathbb {Z}G

is the integral group ring of

G
G

and

H
H

is a finite group of units of augmentation one of

Z

G

\mathbb {Z}G

, then there exists a rational unit

γ
\gamma

such that

H
γ

⊆
G

{H^\gamma } \subseteq G

.
An estimate for coefficients of polynomials in 𝐿²-norm
Authors: Milovanović Gradimir V. , Guessab Allal
Published: June 2010

Let

P

n

{\mathcal {P}_n}

be the class of algebraic polynomials

P
(
x
)
=

∑

v
=
0

n

a
ν

x
ν

P(x) = \sum \nolimits _{v = 0}^n {{a_\nu }{x^\nu }}

of degree at most

n
n

and
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartAbsoluteValue EndAbsoluteValue upper P StartAbsoluteValue EndAbsoluteValue Subscript d sigma Baseline equals left-parenthesis integral Underscript double-struck upper R Endscripts StartAbsoluteValue upper P left-parenthesis x right-parenthesis EndAbsoluteValue squared d sigma left-parenthesis x right-parenthesis right-parenthesis Superscript 1 slash 2">

|

|

P

|

|

d
σ

=

(

∫

R

|

P
(
x
)

|

2

d
σ
(
x
)

)

1

/

2

||P|{|_{d\sigma }} = {({\smallint _\mathbb {R}}|P(x){|^2}d\sigma (x))^{1/2}}

, where

d
σ
(
x
)

d\sigma (x)

is a nonnegative measure on

R

\mathbb {R}

. We determine the best constant in the inequality
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartAbsoluteValue a Subscript nu Baseline EndAbsoluteValue less-than-or-slanted-equals upper C Subscript n comma nu Baseline left-parenthesis d sigma right-parenthesis StartAbsoluteValue EndAbsoluteValue upper P StartAbsoluteValue EndAbsoluteValue Subscript d sigma">

|

a
ν

|

⩽

C

n
,
ν

(
d
σ
)

|

|

P

|

|

d
σ

|{a_\nu }| \leqslant {C_{n,\nu }}(d\sigma )||P|{|_{d\sigma }}

, for

ν
=
n

\nu = n

and

ν
=
n
−
1

\nu = n - 1

, when

P
∈

P

n

P \in {\mathcal {P}_n}

and such that

P
(

ξ
k

)
=
0
,

k
=
1
,
…
,
m

P({\xi _k}) = 0,\;k = 1, \ldots ,m

. The case

d
σ
(
t
)
=
d
t

d\sigma (t) = dt

on

[
−
1
,
1
]

[ - 1,1]

and

P
(
1
)
=
0

P(1) = 0

was studied by Tariq. In particular, we consider the cases when the measure

d
σ
(
x
)

d\sigma (x)

corresponds to the classical orthogonal polynomials on the real line

R

\mathbb {R}

.
Ricci curvature and holomorphic convexity in Kähler manifolds
Authors: Pinney Karen R.
Published: June 2010

In this paper we show that if a smoothly bounded, relatively compact domain in a complex manifold admits a complete Kähler metric with certain bounds on its Ricci tensor, then the domain must be holomorphically convex. This gives an obstruction for the existence of a complete Kähler-Einstein metric on such domains.
The discrete Schwarz-Pick lemma for overlapping circles
Authors: Van Eeuwen Jeff
Published: June 2010

Let P and

P
′

P’

be circle packings in the hyperbolic plane such that they are combinatorically equivalent, neighboring circles in P overlap one another at some fixed angle between 0 and

π

/

2

\pi /2

and the corresponding pairs of circles in

P
′

P’

overlap at the same angle, and the radius for any boundary circle of P is less than or equal to that of the corresponding boundary circle of

P
′

P’

. In this paper we show that the radius of any interior circle of P is less than or equal to that of the corresponding circle in

P
′

P’

, and the hyperbolic distance between the centers of circles in P is less than or equal to the distance between the corresponding circles in

P
′

P’

. Furthermore, a single instance of finite equality in either of the above implies equality for all.
Full subalgebras of Jordan-Banach algebras and algebra norms on 𝐽𝐵*-algebras
Authors: Pérez J. , Rico L. , Rodríguez A.
Published: June 2010

We introduce normed Jordan Q-algebras, namely, normed Jordan algebras in which the set of quasi-invertible elements is open, and we prove that a normed Jordan algebra is a Q-algebra if and only if it is a full subalgebra of its completion. Homomorphisms from normed Jordan Q-algebras onto semisimple Jordan-Banach algebras with minimality of norm topology are continuous. As a consequence, the topology of the norm of a

J

B
∗

J{B^ \ast }

-algebra is the smallest normable topology making the product continuous, and

J

B
∗

J{B^ \ast }

-algebras have minimality of the norm. Some applications to (associative)

C
∗

{C^ \ast }

-algebras are also given: (i) the associative normed algebras that are ranges of continuous (resp. contractive) Jordan homomorphisms from

C
∗

{C^ \ast }

-algebras are bicontinuously (resp. isometrically) isomorphic to

C
∗

{C^ \ast }

-algebras, and (ii) weakly compact Jordan homomorphisms from

C
∗

{C^ \ast }

-algebras are of finite rank.
A class of maps in an algebra with indefinite metric
Authors: Mingarelli Angelo B.
Published: June 2010

We study a class of hermitian maps on an algebra endowed with an indefinite inner product. We show that, in particular, the existence of a non-real eigenvalue is incompatible with the existence of a real eigenvalue having a right-invertible eigenvector. It also follows that for this class of maps the existence of an appropriate extremal for an indefinite Rayleigh quotient implies the nonexistence of nonreal eigenvalues. These results are intended to complement the Perron-Fröbenius and Kreĭn-Rutman theorems, and we conclude the paper by describing applications to ordinary and partial differential equations and to tridiagonal matrices.
Question of global asymptotic stability in state-varying nonlinear systems
Authors: Shih Mau-Hsiang , Wu Jinn Wen
Published: June 2010

A problem raised by LaSalle (i.e., a discrete counterpart of the Jacobian problem in differential equations) concerning the global asymptotic stability in state-varying nonlinear systems is settled. A global asymptotic stability criterion for state-varying systems based on vector energy functions is introduced.
Central sequences in subfactors. II
Authors: Bisch Dietmar
Published: June 2010

We studied in On the existence of central sequences in subfactors [Trans. Amer. Math. Soc. 321 (1990), 117-128] certain ergodicity properties of inclusions of

II
1

{\text {II}_1}

factors

N
⊂
M

N \subset M

. We give here various explicit examples of pairs of

II
1

{\text {II}_1}

factors

N
⊂
M

N \subset M

which have or do not have these properties. In particular, we show that if

N
⊂
M

N \subset M

are hyperfinite

II
1

{\text {II}_1}

factors with finite Jones’s index, then both situations may occur.
A Bernstein-type inequality for the Jacobi polynomial
Authors: Chow Yunshyong , Gatteschi L. , Wong R.
Published: June 2010

Let

P
n

(
α
,
β
)

(
x
)

P_n^{(\alpha ,\beta )}(x)

be the Jacobi polynomial of degree n. For

−

1
2

≤
α
,
β
≤

1
2

- \frac {1}{2} \leq \alpha ,\beta \leq \frac {1}{2}

, and

0
≤
θ
≤
π

0 \leq \theta \leq \pi

, it is proved that
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis sine StartFraction theta Over 2 EndFraction right-parenthesis Superscript alpha plus one half Baseline left-parenthesis cosine StartFraction theta Over 2 EndFraction right-parenthesis Superscript beta plus one half Baseline StartAbsoluteValue upper P Subscript n Superscript left-parenthesis alpha comma beta right-parenthesis Baseline left-parenthesis cosine theta right-parenthesis EndAbsoluteValue less-than-or-equal-to StartFraction normal upper Gamma left-parenthesis q plus 1 right-parenthesis Over normal upper Gamma left-parenthesis one half right-parenthesis EndFraction StartBinomialOrMatrix n plus q Choose n EndBinomialOrMatrix upper N Superscript negative q minus one half Baseline comma">

(
sin
⁡

θ
2

)

α
+

1
2

(
cos
⁡

θ
2

)

β
+

1
2

|

P
n

(
α
,
β
)

(
cos
⁡
θ
)

|

≤

Γ
(
q
+
1
)

Γ
(

1
2

)

(

n
+
q

n

)

N

−
q
−

1
2

,

{(\sin \frac {\theta }{2})^{\alpha + \frac {1}{2}}}{(\cos \frac {\theta }{2})^{\beta + \frac {1}{2}}}|P_n^{(\alpha ,\beta )}(\cos \theta )| \leq \frac {{\Gamma (q + 1)}}{{\Gamma (\frac {1}{2})}}\left ( {\begin {array}{*{20}{c}} {n + q} \\ n \\ \end {array} } \right ){N^{ - q - \frac {1}{2}}},

\]
where

q
=
max
(
α
,
β
)

q = \max (\alpha ,\beta )

and

N
=
n
+

1
2

(
α
+
β
+
1
)

N = n + \frac {1}{2}(\alpha + \beta + 1)

. When

α
=
β
=
0

\alpha = \beta = 0

, this reduces to a sharpened form of the well-known Bernstein inequality for the Legendre polynomial.
A duality theorem for interpolation methods associated to polygons
Authors: Cobos Fernando , Fernández-Martínez Pedro
Published: June 2010

We investigate dual spaces of interpolation spaces defined by means of polygons. We first show that dual spaces may fail to be intermediate spaces with respect to the dual N-tuple, and then we prove that dual spaces of J-spaces can be identified with closed subspaces of K-spaces generated by the dual N-tuple.
Gauge invariant functions of connections
Authors: Sengupta Ambar
Published: June 2010

It is shown that, for certain gauge groups, central functions of the holonomy variables do not determine connections up to gauge equivalence. It is also shown that, for a large class of compact groups, such functions do determine connections up to gauge equivalence. It is then shown that, for the latter type of gauge groups, the Euclidean quantum gauge field measure is determined by the expectation values of the Wilson loop variables (products of characters evaluated on holonomies).
Cyclic approximation of irrational rotations
Authors: Iwanik A.
Published: June 2010

We prove that an irrational number

α
\alpha

admits a rational approximation

|

α
−
p

/

q

|

=
o
(
f
(
q
)
)

|\alpha - p/q| = o(f(q))

iff the irrational rotation

T
x
=
{
x
+
α
}

Tx = \{ x + \alpha \}

admits cyclic approximation with speed

o
(
f
(
n
)
)

o(f(n))

. As an application to earlier results we obtain that a generic Anzai skew product over every irrational rotation is rank-1 and for a.e.

α
\alpha

most skew products admit cyclic approximation with speed

o
(
1

/

n
2

log
⁡
n
)

o(1/{n^2}\log n)

.
Remainders of compactifications and their relation to a quotient lattice of the topology
Authors: Faulkner G. D. , Vipera M. C.
Published: June 2010

If

α
X

\alpha X

is a compactification of a locally compact space X, then the remainder associated with

α
X

\alpha X

is the space

α
X
∖
X

\alpha X\backslash X

. Frequently spaces which are quite different may have families of remainders which are related. This must be reflected somehow in the structure of the spaces. This paper studies one possible formulation of that similarity and its consequences.
A free boundary focusing problem
Authors: Hilhorst Danielle , Hulshof Josephus
Published: June 2010

We consider a one-dimensional free boundary problem arising in combustion theory and establish that all solutions are asymptotically equal to a similarity solution which vanishes in a finite time.
Analyticity of functions and subalgebras of 𝐿^{∞} containing 𝐻^{∞}
Authors: Chang S.-Y. , Garnett J.
Published: June 2010

Let B be a subalgebra of

L
∞

{L^\infty }

containing

H
∞

{H^\infty }

. We give some necessary and sufficient conditions, expressed in terms of analyticity, for a function in

L
∞

{L^\infty }

to belong to B.
Paracompactness of Pixley-Roy hyperspaces. II
Authors: Tanaka Hidenori
Published: June 2010

In this paper we will study the paracompactness of Pixley-Roy hyperspaces of products. We will prove that if

F

[
X
]

\mathcal {F}\left [ X \right ]

is paracompact (resp. hereditarily paracompact), then

F

[

X
2

]

\mathcal {F}\left [ {{X^2}} \right ]

is paracompact (resp. hereditarily paracompact). This is the positive answer to T. Przymusiński’s problem.
Generic bifurcation of periodic points
Authors: Meyer K. R.
Published: June 2010

This paper discusses the bifurcation of periodic points of a generic symplectic diffeomorphism of a two manifold that depends on a parameter. A complete classification of the types of bifurcation that can occur in the generic case is given.
Flat modules over commutative noetherian rings
Authors: Vasconcelos Wolmer V.
Published: June 2010

In this work we study flat modules over commutative noetherian rings under two kinds of restriction: that the modules are either submodules of free modules or that they have finite rank. The first ones have nicely behaved annihilators: they are generated by idempotents. Among the various questions related to flat modules of finite rank, emphasis is placed on discussing conditions implying its finite generation, as for instance, (i) over a local ring, a flat module of constant rank is free, and (ii) a flat submodule of finite rank of a free module is finitely generated. The rank one flat modules already present special problems regarding its endomorphism ring; in a few cases it is proved that they are flat over the base ring. Finally, a special class of flat modules—unmixed—is discussed, which have, so to speak, its source of divisibility somewhat concentrated in the center of its endomorphism ring and thus resemble projective modules over flat epimorphic images of the base ring.
Zero-one laws for Gaussian processes
Authors: Kallianpur G.
Published: June 2010

Some zero-one laws are proved for Gaussian processes defined on linear spaces of functions. They are generalizations of a result for Wiener measure due to R. H. Cameron and R. E. Graves. The proofs exploit an interesting relationship between a Gaussian process and its reproducing kernel Hilbert space. Applications are discussed.
Quadratic variation of potentials and harmonic functions
Authors: Brosamler Gunnar A.
Published: June 2010

We prove the existence of a finite quadratic variation for stochastic processes

u
(
Y
)

u(Y)

, where Y is Brownian motion on a Green domain of

R
n

{R^n}

, stopped upon reaching the Martin boundary, and u is a positive superharmonic function on the domain. As by-products we have results which are also of interest from a non-probabilistic point of view.
Harmonic analysis on nilmanifolds
Authors: Brezin Jonathan
Published: June 2010

We compute, using a device of A. Weil, an explicit decomposition of

L
2

{L^2}

of a nilmanifold into irreducible translation-invariant subspaces. The results refine previous work of C. C. Moore and L. Green.
Some strict inclusions between spaces of 𝐿^{𝑝}-multipliers
Authors: Price J. F.
Published: June 2010

Suppose that the Hausdorff topological group

G
G

is either compact or locally compact abelian and that

C
c

{C_c}

denotes the set of continuous complex-valued functions on

G
G

with compact supports. Let

L
p
q

L_p^q

denote the restrictions to

C
c

{C_c}

of the continuous linear operators from

L
p

(
G
)

{L^p}(G)

into

L
q

(
G
)

{L^q}(G)

which commute with all the right translation operators. When

1
≦
p
>
q
≦
2

1 \leqq p > q \leqq 2

or

2
≦
q
>
p
≦
∞

2 \leqq q > p \leqq \infty

it is known that
\[

(
1
)

L
p
p

⊂

L
q
q

.

(1)\quad L_p^p \subset L_q^q.

\]
The main result of this paper is that the inclusion in (1) is strict unless

G
G

is finite. In fact it will be shown, using a partly constructive proof, that when

G
G

is infinite
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="union Underscript 1 less-than-over-equals q greater-than p Endscripts upper L Subscript q Superscript q subset-of-above-not-equals upper L Subscript p Superscript p subset-of-above-not-equals intersection Underscript p greater-than q less-than-over-equals 2 Endscripts upper L Subscript q Superscript q">

⋃

1
≦
q
>
p

L
q
q

⫋

L
p
p

⫋

⋂

p
>
q
≦
2

L
q
q

\bigcup \limits _{1 \leqq q > p} {L_q^q \subsetneqq } L_p^p \subsetneqq \bigcap \limits _{p > q \leqq 2} {L_q^q}

\]
for

1
>
p
>
2

1 > p > 2

, with the first inclusion remaining strict when

p
=
2

p = 2

and the second inclusion remaining strict when

p
=
1

p = 1

. (Similar results also hold for

2
≦
p
≦
∞

2 \leqq p \leqq \infty

.) When

G
G

is compact, simple relations will also be developed between idempotent operators in

L
p
q

L_p^q

and lacunary subsets of the dual of

G
G

which will enable us to find necessary conditions so that inclusion (1) is strict even if, for example,

L
p
p

L_p^p

and

L
q
q

L_q^q

are replaced by the sets of idempotent operators in

L
p
p

L_p^p

and

L
q
q

L_q^q

respectively.
Whitehead products as images of Pontrjagin products
Authors: Arkowitz Martin
Published: June 2010

A method is given for computing higher order Whitehead products in the homotopy groups of a space

X
X

. If

X
X

can be embedded in an

H
H

-space

E
E

such that the pair

(
E
,
X
)

(E,X)

has sufficiently high connectivity, then we prove that a higher order Whitehead product element in the homotopy of

X
X

is the homomorphic image of a Pontrjagin product in the homology of

E
E

. The two main applications determine a higher order Whitehead product element in (1)

π
∗

(
B

U
t

)

{\pi _ \ast }(B{U_t})

, the homotopy groups of the classifying space of the unitary group

U
t

{U_t}

, (2) the homotopy groups of a space with two nonvanishing homotopy groups.
The space of retractions of the 2-sphere and the annulus
Authors: Wagner Neal R.
Published: June 2010

Given a manifold

M
M

, there is an embedding

Λ
\Lambda

of

M
M

into the space of retractions of

M
M

, taking each point to the retraction of

M
M

to that point. Considering

Λ
\Lambda

as a map into the connected component containing its image, we prove that

Λ
\Lambda

is a weak homotopy equivalence for two choices of

M
M

, namely, the

2
2

-sphere and the annulus.
Algebraic models for probability measures associated with stochastic processes
Authors: Schreiber B. M. , Sun T.-C. , Bharucha-Reid A. T.
Published: June 2010

This paper initiates the study of probability measures corresponding to stochastic processes based on the Dinculeanu-Foiaş notion of algebraic models for probability measures. The main result is a general extension theorem of Kolmogorov type which can be summarized as follows: Let

{
(
X
,

A

i

,

μ
i

)
,
i
∈
I
}

\{ (X,{\mathcal {A}_i},{\mu _i}),i \in I\}

be a directed family of probability measure spaces. Then there is an associated directed family of probability measure spaces

{
(
G
,

B

i

,

v
i

)
,
i
∈
I
}

\{ (G,{\mathcal {B}_i},{v_i}),i \in I\}

and a probability measure

v
v

on the

σ
\sigma

-algebra

B

\mathcal {B}

generated by the

B

i

{\mathcal {B}_i}

such that (i)

v
(
B
)
=

v
i

(
B
)
,
B
∈

B

i

,
i
∈
I

v(B) = {v_i}(B),B \in {\mathcal {B}_i},i \in I

, and (ii) for each is

i
∈
I

i \in I

the spaces

(
X
,

A

i

,

μ
i

)

(X,{\mathcal {A}_i},{\mu _i})

and

(
G
,

B

i

,

v
i

)

(G,{\mathcal {B}_i},{v_i})

are conjugate. The importance of the main theorem is that under certain mild conditions there exists an embedding

ψ
:
X
→
G

\psi :X \to G

such that the induced measures

v
i

{v_i}

on

G
G

are extendable to

v
v

, although the measures

μ
i

{\mu _i}

on

X
X

may not be extendable. Using the algebraic model formulation, the Kolmogorov extension property and the notion of a representation of a directed family of probability measure spaces are discussed.
Word problem for ringoids of numerical functions
Authors: Iskander A.
Published: June 2010

A. The composition ringoid of functions on (i) the positive integers, (ii) all integers, (iii) the reals and (iv) the complex numbers, do not satisfy any identities other than those satisfied by all composition ringoids. B. Given two words

u
,
υ

u,\upsilon

of the free ringoid, specific functions on the positive integers,

f
1

,
…
,

f
k

{f_1}, \ldots ,{f_k}

can be described such that

u
(

f
1

,
…
,

f
k

)

u({f_1}, \ldots ,{f_k})

and

υ
(

f
1

,
…
,

f
k

)

\upsilon ({f_1}, \ldots ,{f_k})

, evaluated at 1, are equal iff

u
=
υ

u = \upsilon

is an identity of the free ringoid.
Prime ideals in a large class of nonassociative rings
Authors: Zwier Paul J.
Published: June 2010

In this paper a definition is given for a prime ideal in an arbitrary nonassociative ring

N
N

under the single restriction that for a given positive integer

s
≧
2

s \geqq 2

, if

A
A

is an ideal in

N
N

, then

A
s

{A^s}

is also an ideal. (

N
N

is called an

s
s

-naring.) This definition is used in two ways. First it is used to define the prime radical of

N
N

and the usual theorems ensue. Second, under the assumption that the

s
s

-naring

N
N

has a certain property

(
α
)

(\alpha )

, the Levitzki radical

L
(
N
)

L(N)

of

N
N

is defined and it is proved that

L
(
N
)

L(N)

is the intersection of those prime ideals

P
P

in

N
N

whose quotient rings are Levitzki semisimple.

N
N

has property

(
α
)

(\alpha )

if and only if for each finitely generated subring

A
A

and each positive integer

m
m

, there is an integer

f
(
m
)

f(m)

such that

A

f
(
m
)

⊆

A
m

{A^{f(m)}} \subseteq {A_m}

. (Here

A
1

=

A
s

{A_1} = {A^s}

and

A

m
+
1

=

A
m
s

{A_{ m + 1}} = A_m^s

.) Furthermore, conditions are given on the identities an

s
s

-naring

N
N

satisfies which will insure that

N
N

satisfies

(
α
)

(\alpha )

. It is then shown that alternative rings, Jordan rings, and standard rings satisfy these conditions.
Embedding a partially ordered ring in a division algebra
Authors: Reynolds William H.
Published: June 2010

D. K. Harrison has shown that if a ring with identity has a positive cone that is an infinite prime (a subsemiring that contains 1 and is maximal with respect to avoiding — 1), and if the cone satisfies a certain archimedean condition for all elements of the ring, then there exists an order isomorphism of the ring into the real field. Our main result shows that if Harrison’s archimedean condition is weakened so as to apply only to the elements of the cone and if a certain centrality relation is satisfied, then there exists an order isomorphism of the ring into a division algebra that is algebraic over a subfield of the real field. Also, Harrison’s result and a related theorem of D. W. Dubois are extended to rings without identity; in so doing, it is shown that order isomorphic subrings of the real field are identical.
Dualities for equational classes of Brouwerian algebras and Heyting algebras
Authors: Davey Brian A.
Published: June 2010

This paper focuses on the equational class

S

n

{{\mathbf {S}}_n}

of Brouwerian algebras and the equational class

L

n

{{\mathbf {L}}_n}

of Heyting algebras generated by an n-element chain. Firstly, duality theories are developed for these classes. Next, the projectives in the dual categories are determined, and then, by applying the dualities, the injectives and absolute subretracts in

S

n

{{\mathbf {S}}_n}

and

L

n

{{\mathbf {L}}_n}

are characterized. Finally, free products and the finitely generated free algebras in

S

n

{{\mathbf {S}}_n}

and

L

n

{{\mathbf {L}}_n}

are described.
Group extensions and cohomology for locally compact groups. IV
Authors: Moore Calvin C.
Published: June 2010

In this paper we shall apply the cohomology groups constructed in [14] to a variety of problems in analysis. We show that cohomology classes admit direct integral decompositions, and we obtain as a special case a new proof of the existence of direct integral decompositions of unitary representations. This also leads to a Frobenius reciprocity theorem for induced modules, and we obtain splitting theorems for direct integrals of tori analogous to known results for direct sums. We also obtain implementation theorems for groups of automorphisms of von Neumann algebras. We show that the splitting group topology on the two-dimensional cohomology groups agrees with other naturally defined topologies and we find conditions under which this topology is

T
2

{T_2}

. Finally we resolve several questions left open concerning splitting groups in a previous paper [13].
A decomposition of weighted translation operators
Authors: Bastian Joseph J.
Published: June 2010

Let (X, A, m) be a measure space and T an invertible measure-preserving transformation on X. Given

ϕ
\phi

in

L
∞

(
X
)

{L^\infty }(X)

, define operators

M
ϕ

{M_\phi }

and

U
T

{U_T}

on

L
2

(
X
)

{L^2}(X)

by

(

M
ϕ

f
)
(
x
)
=
ϕ
(
x
)
f
(
x
)

({M_\phi }f)(x) = \phi (x)f(x)

and

(

U
T

f
)
=
f
(
T
x
)

({U_T}f) = f(Tx)

. Operators of the form

M
ϕ

U
T

{M_\phi }{U_T}

are called weighted translation operators. In this paper it is shown that every weighted translation operator on a sufficiently regular measure space an be decomposed into a direct integral of weighted translation operators where almost all of the transformations in the integrand are ergodic. It is also shown that every hyponormal weighted translation operator defined by an ergodic transformation is either normal or unitarily equivalent to a bilateral weighted shift. These two results along with some results concerning direct integrals of hyponormal and subnormal operators are used to show that every hyponormal (resp. subnormal) weighted translation operator is unitarily equivalent to a direct integral of normal operators and hyponormal (resp. subnormal) bilateral weighted shifts. The paper concludes with an example.
Analysis with weak trace ideals and the number of bound states of Schrödinger operators
Authors: Simon Barry
Published: June 2010

We discuss interpolation theory for the operator ideals

I
p
w

I_p^w

defined on a separable Hilbert space as those operators A whose singular values

μ
n

(
A
)

{\mu _n}(A)

obey

μ
n

⩽
c

n

−
1

/

p

{\mu _n} \leqslant c{n^{ - 1/p}}

for some c. As an application we consider the functional

N
(
V
)
=
dim

N(V) = \dim

(spectral projection on

(
−
∞
,
0
)

( - \infty ,0)

for

−
Δ
+
V

- \Delta + V

) on functions V on

R

n

,
n
⩾
3

{{\mathbf {R}}^n},n \geqslant 3

. We prove that for any
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="epsilon greater-than 0 colon upper N left-parenthesis upper V right-parenthesis less-than-or-slanted-equals upper C Subscript epsilon Baseline left-parenthesis double-vertical-bar upper V double-vertical-bar Subscript n slash 2 plus epsilon Baseline plus double-vertical-bar upper V double-vertical-bar Subscript n slash 2 minus epsilon Baseline right-parenthesis Superscript n slash 2">

ϵ
>
0
:
N
(
V
)
⩽

C
ϵ

(

‖
V
‖

n

/

2
+
ϵ

+

‖
V
‖

n

/

2
−
ϵ

)

n

/

2

\epsilon > 0:N(V) \leqslant C_\epsilon (\left \| V \right \|_{n/2 + \epsilon } + \left \| V \right \|_{n/2 - \epsilon })^{n/2}

where

‖
⋅
‖

p

{\left \| \cdot \right \|_p}

is an

L
p

{L^p}

norm and that
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="limit Underscript lamda right-arrow normal infinity Endscripts upper N left-parenthesis lamda upper V right-parenthesis slash lamda Superscript n slash 2 Baseline equals left-parenthesis 2 pi right-parenthesis Superscript negative n Baseline tau Subscript n Baseline integral StartAbsoluteValue upper V Subscript minus Baseline left-parenthesis x right-parenthesis EndAbsoluteValue Superscript n slash 2 Baseline d Superscript n Baseline x">

lim

λ
→
∞

N
(
λ
V
)

/

λ

n

/

2

=

(
2
π

)

−
n

τ
n

∫

|

V
−

(
x
)

|

n

/

2

d
n

x

{\lim \nolimits _{\lambda \to \infty }}N(\lambda V)/{\lambda ^{n/2}} = {(2\pi )^{ - n}}{\tau _n}\smallint |{V_ - }(x){|^{n/2}}{d^n}x

for any

V
∈

L

n

/

2
−

∩

L

n

/

2
+

V \in {L^{n/2 - }} \cap {L^{n/2 + }}

. Here

V
−

{V_ - }

is the negative part of V and

τ
n

{\tau _n}

is the volume of the unit ball in

R

n

{{\mathbf {R}}^n}

.
A Plancherel formula for idyllic nilpotent Lie groups
Authors: Carlton Eloise
Published: June 2010

A procedure is developed which can be used to compute the Plancherel measure for a certain class of nilpotent Lie groups, including the Heisenberg groups, free groups, two-and three-step groups, the nilpotent part of an Iwasawa decomposition of the R-split form of the classical simple groups

A
l

,

C
l

,

G
2

{A_l},{C_l},{G_2}

. Let G be a connected, simply connected nilpotent Lie group. The Plancherel formula for G can be expressed in terms of Plancherel measure of a normal subgroup N and projective Plancherel measures of certain subgroups of

G

/

N

G/N

. To get an explicit measure for G, we need an explicit formula for (1) the disintegration of Plancherel measure of N under the action of G on N, and (2) projective Plancherel measures of

G
γ

/

N

{G_\gamma }/N

, where

G
γ

{G_\gamma }

is the stability subgroup at

γ
\gamma

in N. When both N and

G
γ

/

N

{G_\gamma }/N

are abelian, the measures (1) and (2) are obtained as special cases of more general problems. These measures combine into Plancherel measure for G.
Associated and skew-orthologic simplexes
Authors: Gerber Leon
Published: June 2010

A set of

n
+
1

n + 1

lines in n-space is said to be associated if every

(
n
−
2
)

(n - 2)

-flat which meets n of the lines also meets the remaining line. Two Simplexes are associated if the joins of their corresponding vertices are associated. Two Simplexes are (skew-)orthologic if the perpendiculars from the vertices of one on the faces of the other are concurrent (associated); it follows that the reciprocal relation holds. In an earlier paper, Associated and Perspective Simplexes, we gave an affine necessary and sufficient condition for two simplexes to be associated that was so easy to apply that extensions to n-dimensions of nearly all known theorems, and a few new ones, were proved in a few lines of calculations. In this sequel we take a closer look at some of the results of the earlier paper and prove some new results. Then we give simple Euclidean necessary and sufficient conditions for two simplexes to be orthologic or skew-orthologic which yield as corollaries known results on altitudes, the Monge point and orthocentric simplexes. We conclude by discussing some of the qualitative differences between the geometries of three and higher dimensions.
Structurally stable Grassmann transformations
Authors: Batterson Steve
Published: June 2010

A Grassmann transformation is a diffeomorphism on a Grassmann manifold which is induced by an

n
×
n

n \times n

nonsingular matrix. In this paper the structurally stable Grassmann transformations are characterized to be the maps which are induced by matrices whose eigenvalues have distinct moduli. There is exactly one topological conjugacy class of complex structurally stable Grassmann transformations. For the real case the topological classification is determined by the ordering (relative to modulus) of the signs of the eigenvalues of the inducing matrix.
Multiplier criteria of Marcinkiewicz type for Jacobi expansions
Authors: Gasper George , Trebels Walter
Published: June 2010

It is shown how an integral representation for the product of Jacobi polynomials can be used to derive a certain integral Lipschitz type condition for the Cesàro kernel for Jacobi expansions. This result is then used to give criteria of Marcinkiewicz type for a sequence to be multiplier of type (p, p),

1
>
p
>
∞

1 > p > \infty

, for Jacobi expansions.
Minimal invariant functions of the space-time Wiener process
Authors: Woo Kai Yuen
Published: June 2010

Minimal invariant functions of the space-time Wiener process are obtained.
A general Stone-Gel’fand duality
Authors: Lambek J. , Rattray B. A.
Published: June 2010

We give a simple characterization of full subcategories of equational categories. If

a

\mathcal {a}

is one such and

B

\mathcal {B}

is the category of topological spaces, we consider a pair of adjoint functors

a

o
p

⟷
U

F

B

{\mathcal {a}^{op}}\underset {F}{\overset {U}{\longleftrightarrow }}\mathcal {B}

which are represented by objects I and J in the sense that the underlying sets of

U
(
A
)

U(A)

and

F
(
B
)

F(B)

are

a

(
A
,
I
)

\mathcal {a}(A,I)

and

B

(
B
,
J
)

\mathcal {B}(B,J)

. (One may take I and J to have the same underlying set.) Such functors always establish a duality between Fix FU and Fix UF. We study conditions under which one can conclude that FU and UF are reflectors into Fix FU and Fix UF, that Fix FU = Image F = the limit closure of I in

a

\mathcal {a}

and that Fix UF = Image U = the limit closure of J in

B

\mathcal {B}

. For example, this happens if (1)

a

\mathcal {a}

is a limit closed subcategory of an equational category, (2) J is compact Hausdorff and has a basis of open sets of the form

{
x
∈
J

|

α
(
I
)
(
x
)
≠
β
(
I
)
(
x
)
}

\{ x \in J|\alpha (I)(x) \ne \beta (I)(x)\}

, where

α
\alpha

and

β
\beta

are unary

a

\mathcal {a}

-operations, and (3) there are quaternary operations

ξ
\xi

and

η
\eta

such that, for all

x
∈

J
4

,
ξ
(
I
)
(
x
)
=
η
(
I
)
(
x
)

x \in {J^4},\xi (I)(x) = \eta (I)(x)

if and only if

x
1

=

x
2

{x_1} = {x_2}

or

x
3

=

x
4

{x_3} = {x_4}

. (The compactness of J may be dropped, but then one loses the conclusion that Fix FU is the limit closure of I.) We also obtain a quite different set of conditions, a crucial one being that J is compact and that every f in

B

(

J
n

,
J
)

\mathcal {B}({J^n},J)

, n finite, can be uniformly approximated arbitrarily closely by

a

\mathcal {a}

-operations on I. This generalizes the notion of functional completeness in universal algebra. The well-known dualities of Stone and Gelfand are special cases of both situations and the generalization of Stone duality by Hu is also subsumed.
Some infinite free boundary problems
Authors: Tepper David E. , Wildenberg Gerald
Published: June 2010

Let

Γ
\Gamma

be the boundary of an unbounded simply connected region

D

\mathcal {D}

, and let

C

(
Γ
)

\mathcal {C}(\Gamma )

denote the family of all simply connected regions

Δ
⊂

D

\Delta \subset \mathcal {D}

such that

∂
Δ
=
Γ
∪
γ

\partial \Delta = \Gamma \cup \gamma

where

γ
∩
Γ

\gamma \cap \Gamma

contains only the infinite point. For

Δ
∈

C

(
Γ
)

\Delta \in \mathcal {C}(\Gamma )

we call

γ
\gamma

the free boundary of

Δ
\Delta

. Given a positive constant

λ
\lambda

, we seek to find a region

Δ
λ

∈

C

(
Γ
)

{\Delta _\lambda } \in \mathcal {C}(\Gamma )

with free boundary

γ
λ

{\gamma _\lambda }

such that there is a bounded harmonic function V in

Δ
λ

{\Delta _\lambda }

with the properties that (i)

V
=
0

V = 0

on

Γ
\Gamma

, (ii)

V
=
1

V = 1

on

γ
\gamma

, (iii)

|

grad 

V
(
z
)

|

=
λ

\left | {{\text {grad }}V(z)} \right | = \lambda

for

z
∈

γ
λ

z \in {\gamma _\lambda }

. We give sufficient conditions for existence and uniqueness of

Δ
λ

{\Delta _\lambda }

. We also give quantitative properties of

γ
λ

{\gamma _\lambda }

.
Center-by-metabelian groups of prime exponent
Authors: Miller Jay I.
Published: June 2010

We show that a center-by-metabelian group of prime exponent p is nilpotent of class at most p, and this result is best possible. The proof is based on techniques dealing with varieties of groups.
Twisted free tensor products
Authors: Katz Elyahu
Published: June 2010

A twisted free tensor product of a differential algebra and a free differential algebra is introduced. This complex is proved to be chain homotopy equivalent to the complex associated with a twisted free product of a simplicial group and a free simplicial group. In this way we turn a geometric situation into an algebraic one, i.e. for the cofibration

Y
→
Y

∪
g

C
X
→
Σ
X

Y \to Y\,{ \cup _g}\,CX \to \Sigma X

we obtain a spectral sequence converging into

H
(
Ω
(
Y

∪
g

C
X
)
)

H(\Omega (Y\,{ \cup _g}\,CX))

. The spectral sequence obtained in the above situation is similar to the one obtained by L. Smith for a cofibration. However, the one we obtain has more information in the sense that differentials can be traced, requires more lax connectivity conditions and does not need the ring of coefficients to be a field.
A noncommutative generalization and 𝑞-analog of the Lagrange inversion formula
Authors: Gessel Ira
Published: June 2010

The Lagrange inversion formula is generalized to formal power series in noncommutative variables. Aq-analog is obtained by applying a linear operator to the noncommutative formula before substituting commuting variables.
On the excursion process of Brownian motion
Authors: Knight Frank B.
Published: June 2010

Let

W
0
+

(
t
)

W_0^ + \,(t)

denote the scaled excursion process of Brownian motion, and let

l
0
+

(
a
)
,

0

⩽

a
,

l_0^ + \,(a),\,0\, \leqslant \,a,

be its local time at a. The joint distribution of

l
0
+

(
a
)
,

β
(
a
)
,

l_0^ + \,(a),\,\beta (a),

and

γ
(
a
)

\gamma (a)

is obtained, where

β
(
a
)

\beta (a)

and

γ
(
a
)

\gamma (a)

are the last exit time and the first passage time of a by

W
0

+

(
t
)

W_0^{ + }\,(t)

.
Fractional differentiation and Lipschitz spaces on local fields
Authors: Onneweer C. W.
Published: June 2010

In this paper we continue our study of differentiation on a local field K. We define strong derivatives of fractional order

α

>

0

\alpha \, > \,0

for functions in

L
r

(

K

)

{L_r}(\textbf {K})

,

1

⩽

r

>

∞

1\, \leqslant \,r\, > \,\infty

. After establishing a number of basic properties for such derivatives we prove that the spaces of Bessel potentials on K are equal to the spaces of strongly

L
r

(

K

)

{L_r}(\textbf {K})

-differentiable functions of order

α

>

0

\alpha \, > \,0

when

1

⩽

r

⩽

2

1\, \leqslant \,r\, \leqslant \,2

. We then focus our attention on the relationship between these spaces and the generalized Lipschitz spaces over K. Among others, we prove an inclusion theorem similar to a wellknown result of Taibleson for such spaces over

R

n

{\textbf {R}^n}

.
On meromorphic solutions of algebraic differential equations
Authors: Strelitz Sh.
Published: June 2010

The Malmquist Theorem is generalized for equations of the type
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper R left-parenthesis z comma w comma w prime comma ellipsis comma w Superscript left-parenthesis n right-parenthesis Baseline right-parenthesis equals upper P left-parenthesis z comma w right-parenthesis slash upper Q left-parenthesis z comma w right-parenthesis">

R
(
z
,

w
,

w
′

,

…

,

w

(
n
)

)

=

P
(
z
,

w
)

/

Q
(
z
,

w
)

R(z,\,w,\,w’,\, \ldots \,,\,{w^{(n)}})\, = \,{{P(z,\,w)}/{Q(z,\,w)}}

where P, Q and R are polynomials of w and

w
,

w
′

,

…

,

w

(
n
)

w,\,w’,\, \ldots \,,\,{w^{(n)}}

respectively with meromorphic coefficients of finite order.
Periodic orbits of continuous mappings of the circle
Authors: Block Louis
Published: June 2010

Let f be a continuous map of the circle into itself and let

P
(
f
)

P(f)

denote the set of positive integers n such that f has a periodic point of period n. It is shown that if

1

∈

P
(
f
)

1\, \in \,P(f)

and

n

∈

P
(
f
)

n\, \in \,P(f)

for some odd positive integer n then for every integer

m

>

n

m\, > \,n

,

m

∈

P
(
f
)

m\, \in \,P(f)

. Furthermore, if

P
(
f
)

P(f)

is finite then there are integers m and n (with

m

⩾

1

m\, \geqslant \,1

and

n

⩾

0

n\, \geqslant \,0

) such that

P
(
f
)

=

{
m
,

2

m
,

4

m
,

8

m
,

…
,

2
n

m
}

P(f)\, = \,\{ m,\,2\,m,\,4\,m,\,8\,m,\,\ldots ,\,{2^n}\,m\}

.
A Radon transform on spheres through the origin in 𝑅ⁿ and applications to the Darboux equation
Authors: Cormack A. M. , Quinto E. T.
Published: June 2010

On domain

C
∞

(

R
n

)

{C^\infty }\,({R^n})

we invert the Radon transform that maps a function to its mean values on spheres containing the origin. Our inversion formula implies that if

f

∈

C
∞

(

R
n

)

f\, \in \,{C^\infty }\,({R^n})

and its transform is zero on spheres inside a disc centered at 0, then f is zero inside that disc. We give functions

f

∉

C
∞

(

R
n

)

f\, \notin \,{C^\infty }\,({R^n})

whose transforms are identically zero and we give a necessary condition for a function to be the transform of a rapidly decreasing function. We show that every entire function is the transform of a real analytic function. These results imply that smooth solutions to the classical Darboux equation are determined by the data on any characteristic cone with vertex on the initial surface; if the data is zero near the vertex then so is the solution. If the data is entire then a real analytic solution with that data exists.
Derivations on algebras of unbounded operators
Authors: Inoue Atsushi , Ota Shôichi
Published: June 2010

This paper is a study of derivations on unbounded operator algebras in connection with those in operator algebras. In particular we study spatiality of derivations in several situations. We give the characterization of derivations on general *-algebras by using positive linear functionals. We also show that a derivation with some range-property on a left

E

W
#

E{W^\# }

-algebra induced by an unbounded Hilbert algebra is strongly implemented by an operator which belongs to an algebra of measurable operators.
Hyperbolic Birkhoff centers
Authors: Malta I. P.
Published: June 2010

The purpose of this paper is to show that if f is a diffeomorphism of a compact manifold whose Birkhoff center,

c
(
f
)

c(f)

, is hyperbolic and has no cycles, then f satisfies Axiom A and is

Ω
\Omega

-stable. To obtain a filtration for

c
(
f
)

c(f)

, the concept of an isolated set for a homeomorphism of a compact metric space is introduced. As a partial converse it is proved that if

c
(
f
)

c(f)

is hyperbolic and f is

Ω
\Omega

-stable, then

c
(
f
)

c(f)

has the no cycle property. A characterization of

Ω
\Omega

-stability when

c
(
f
)

c(f)

is finite is also given.
*-valuations and ordered *-fields
Authors: Holland Samuel S.
Published: June 2010

We generalize elementary valuation theory to *-fields (division rings with involution), apply the generalized theory to the task of ordering *-fields, and give some applications to Hermitian forms.
Splitting criteria for 𝔤-modules induced from a parabolic and the Berňsteĭn-Gel’fand-Gel’fand resolution of a finite-dimensional, irreducible 𝔤-module
Authors: Rocha-Caridi Alvany
Published: June 2010

Let

g

\mathcal {g}

be a finite dimensional, complex, semisimple Lie algebra and let V be a finite dimensional, irreducible

g

\mathcal {g}

-module. By computing a certain Lie algebra cohomology we show that the generalized versions of the weak and the strong Bernstein-Gelfand-Gelfand resolutions of V obtained by H. Garland and J. Lepowsky are identical. Let G be a real, connected, semisimple Lie group with finite center. As an application of the equivalence of the generalized Bernstein-Gelfand-Gelfand resolutions we obtain a complex in terms of the degenerate principal series of G, which has the same cohomology as the de Rham complex.
The product of two countably compact topological groups
Authors: van Douwen Eric K.
Published: June 2010

We use MA ( = Martin’s Axiom) to construct two countably compact topological groups whose product is not countably compact. To this end we first use MA to construct an infinite countably compact topological group which has no nontrivial convergent sequences.
𝐿^{𝑝} behavior of certain second order partial differential operators
Authors: Kenig Carlos E. , Tomas Peter A.
Published: June 2010

We give examples of bounded inverses of polynomials in

R

n

{{\textbf {R}}^n}

,

n

>

1

n\, > \,1

, which are not Fourier multipliers of

L
p

(

R

n

)

{L^p}\,({{\textbf {R}}^n})

for any

p

≠

2

p\, \ne \,2

. Our main tool is the Kakeya set construction of C. Fefferman. Using these results, we relate the invertibility on

L
p

{L^p}

of a linear second order constant coefficient differential operator D on

R

n

{{\textbf {R}}^n}

to the geometric structure of quadratic surfaces associated to its symbol d. This work was motivated by multiplier conjectures of N. Rivière and R. Strichartz.
Maximum principles for degenerate elliptic-parabolic equations with Venttsel’s boundary condition
Authors: Amano Kazuo
Published: June 2010

In this paper, we first establish interior and boundary maximum principles for degenerate elliptic-parabolic equations; we state both principles in one single theorem in terms of the propagation set (cf. Theorem 1). We next generalize the boundary condition to Venttsel’s one and obtain the similar result (cf. Theorem 2). Venttsel”s boundary condition contains Dirichlet, Neumann, oblique derivative and mixed boundary conditions as special cases and, from a probabilistic point of view (cf. Venttsel’ [9]), it is the most general admissible boundary condition. We give several examples in the last section.
Localizable analytically uniform spaces and the fundamental principle
Authors: Hansen Sönke
Published: June 2010

The Fundamental Principle of Ehrenpreis states that the solutions of homogeneous linear partial differential equations with constant coefficients have natural integral representations. Using the Oka-Cartan procedure Ehrenpreis derived this theorem for spaces of functions and distributions which he called localizable analytically uniform (LAU-spaces). With a new definition of LAU-spaces we explain how Hörmander’s results on cohomology with bounds fit into Ehrenpreis’ method of proof of the Fundamental Principle. Furthermore, we show that many of the common Fréchet-Montel spaces of functions are LAU-spaces.
Algebraic invariants of boundary links
Authors: Sato Nobuyuki
Published: June 2010

In this paper we study the homology of the universal abelian cover of the complement of a boundary link of

n
n

-spheres in

S

n
+
2

{S^{n + 2}}

, as modules over the (free abelian) group of covering transformations. A consequence of our results is a characterization of the polynomial invariants

p

i
,
q

{p_{i,q}}

of boundary links for

1
⩽
q
⩽
[
n

/

2
]

1 \leqslant q \leqslant [n/2]

. Along the way we address the following algebraic problem: given a homomorphism of commutative rings

f
:
R
→
S

f:R \to S

and a chain complex

C
∗

{C_ \ast }

over

R
R

, determine when the complex

S

⊗
R

C
∗

S{ \otimes _R}{C_ \ast }

is acyclic. The present work is a step toward the characterization of link modules in general.