pinecone/core-2020-05-10-deduplication huggingface dataset:
Strong Stability of Bounded Evolution Families and Semigroups

AbstractWe prove several characterizations of strong stability of uniformly bounded evolution families (U(t,s))t⩾s⩾0 of bounded operators on a Banach space X, i.e. we characterize the property limt→∞ ∥U(t,s)x∥=0 for all s⩾0 and all x∈X. These results are connected to the asymptotic stability of the well-posed linear nonautonomous Cauchy problemu(t)=A(t)u(t),t⩾s⩾0,u(s)=x,x∈X.In the autonomous case, i.e. when U(t,s)=T(t−s) for some C0-semigroup (T(t))t⩾0, we present, in addition, a range condition on the generator A of (T(t))t⩾0 which is sufficient for strong stability. This condition is more general than the condition in the ABLV-Theorem involving countability of the imaginary part of the spectrum of A
Differentiation in Star-Invariant Subspaces II. Schatten Class Criteria

AbstractGiven an inner function θ on the upper half-plane C+, let Kθ≔H2⊖θH2 be the corresponding star-invariant subspace of the Hardy space H2. Earlier we showed that the differentiation operator ddx: Kθ→L2(R) is bounded iff θ′∈L∞(R) and compact iff θ′∈C0(R). The current problem is to determine when the above operator belongs to the Schatten–von Neumann class Sp. The most important cases are p=1 and p=2, and for these p's we solve the problem completely. The S1 and S2 criteria that arise involve the decay rate of θ′ at infinity or (alternatively) the distribution of the zero sequence {zj} of θ. Moreover, explicit formulae for the trace and the Hilbert–Schmidt norm are provided. For other values of p, we point out some necessary and some sufficient conditions in order that ddx∈Sp. The gap is presumably quite small, and we are able to eliminate it for special classes of zero sequences {zj}
Uniqueness Results for the Generators of the Two-Dimensional Euler and Navier–Stokes Flows

AbstractThe Euler and Navier–Stokes equations for an incompressible fluid in two dimensions with periodic boundary conditions are considered. Concerning the Euler equation, previous works analyzed the associated (first order) Liouville operator L as a symmetric linear operator in a Hilbert space L2(μγ) with respect to a natural invariant Gaussian measure μγ (given by the enstrophy), with the domain subspace of cylinder smooth bounded functions and have shown that there exist self-adjoint extensions of L. For the Navier–Stokes equation with a suitable white noise forcing term, the associated (second order) Kolmogorov operator K has been considered on the same domain as the sum of the Liouville operator L with the Ornstein–Uhlenbeck operator Q corresponding to the Stokes operator and the forcing term; existence of a C0-semigroup of contraction in L2(μγ) with generator extending the operator K has been proven. In this paper it is proven that both L and K are bounded by naturally associated positive Schrödinger-like operators, which are essentially self-adjoint on a dense subspace of cylinder functions. Other uniqueness results concerning L, respectively, K are also given
The Periodic Schrödinger Operators with Potentials in the Morrey Class

AbstractWe consider the periodic Schrödinger operator −Δ+V(x) in Rd, d⩾3 with potential V in the Morrey class. Let Ω be a periodic cell for V. We show that, for p∈((d−1)/2,d/2], there exists a positive constant ε depending only on the shape of Ω, p and d such that, iflim supr→0supx∈Ωr21∣B(x,r)∣∫B(x,r)∣V(y)∣pdy1/p<ε, then the spectrum of −Δ+V is purely absolutely continuous. We obtain this result as a consequence of certain weighted L2 Sobolev inequalities on the d-torus. It improves an early result by the author for potentials in Ld/2 or weak-Ld/2 space
Invariant Hyperfunction Solutions to Invariant Differential Equations on the Space of Real Symmetric Matrices

AbstractThe real special linear group of degree n naturally acts on the vector space of n×n real symmetric matrices. How to determine invariant hyperfunction solutions of invariant linear differential equations with polynomial coefficients on the vector space of n×n real symmetric matrices is discussed in this paper. We prove that every invariant hyperfunction solution is expressed as a linear combination of Laurent expansion coefficients of the complex power of the determinant function with respect to the parameter of the power. Then the problem is reduced to the determination of Laurent expansion coefficients
Classification of Simple C*-Algebras: Inductive Limits of Matrix Algebras Over One-Dimensional Spaces

AbstractIn this article, we will give a complete classification of simple C*-algebras which can be written as inductive limits of algebras of the form An=⊕i=1knM[n,i](C(Xn,i)), where Xn,i are arbitrary variable one-dimensional compact metrizable spaces. The results unify and generalize the previous results for the case Xn,i=S1 and for the case of Xn,i being trees. We obtain our classification results by reducing the case of general one-dimensional spaces to the case of circles. The techniques in this paper play important roles in the study of the case of higher-dimensional spaces
The Structure of Inner Multipliers on Spaces with Complete Nevanlinna Pick Kernels

AbstractLet k be the reproducing kernel for a Hilbert space H(k) of analytic functions on Bd, the open unit ball in Cd, d⩾1. k is called a complete NP kernel if k0≡1 and if 1−1/kλ(z) is positive definite on Bd×Bd. Let D be a separable Hilbert space, and consider H(k)⊗D≅H(k,D), and think of it as a space of D-valued H(k)-functions. A theorem of McCullough and Trent (J. Funct. Anal.178 (2000), 226–249) partially extends the Beurling–Lax–Halmos theorem for the invariant subspaces of the Hardy space H2(D). They show that if k is a complete NP kernel and if D is a separable Hilbert space, then for any scalar multiplier invariant subspace M of H(k,D) there exists an auxiliary Hilbert space E and a multiplication operator φ: H(k,E)→H(k,D) such that φ is a partial isometry and M=φH(k,E). Such multiplication operators are called inner multiplication operators and they satisfy φφ;*=the orthogonal projection onto M. In this paper, we shall show that for many interesting complete NP kernels the analogy with the Beurling–Lax–Halmos theorem can be strengthened. We show that for almost every z∈∂Bd the nontangential limit φ(z) of the multiplier φ:Bd→B(E,D) associated with an inner multiplication operator φ is a partial isometry and that rank φ(z) is equal to a constant almost everywhere. The result applies to certain weighted Dirichlet spaces and to the space H2d, which is determined by the kernel kλ(z)=11−〈z,λ〉d ,λ,z∈Bd. In particular, our result implies that the curvature invariant of Arveson (Proc. Natl. Acad. Sci. USA96 (1999), 11,096–11,099) of a pure contractive Hilbert module of finite rank is an integer. This answers a question of W. Arveson (Proc. Natl Acad. Sci. USA96 (1999), 11096–11099)
Extremal Growth of Powers of Operators Satisfying Resolvent Conditions of Kreiss-Ritt Type

AbstractLet E be a compact subset of the unit circle. We determine the extremal rate of growth of (∥Tn∥)n⩾1 for Banach-space operators T satisfying the resolvent condition∥(T−λI)−1∥⩽const.dist(λ,E)(∣λ∣1) . This includes, as extreme cases, the Kreiss condition E=T and the Ritt condition E={1}. For intermediate sets E, the cardinality, the measure and the Hausdorff dimension of E all play a rôle in determining the growth of ∥Tn∥. As a by-product, we also obtain lower bounds for the Taylor coefficients of functions f holomorphic on the unit disk and satisfying∣f(z)∣⩾1dist(z,E)(∣z∣<1)
Planar Depth and Planar Subalgebras

AbstractWe consider the notion of planar depth of a planar algebra, viz., the smallest n for which the planar algebra is generated by its ‘n-boxes’. We establish a simple result which yields a sufficient condition, in terms of the principal graph of the planar algebra, for the planar depth to be bounded by k. This suffices to determine the planar depth of the E6, E8 and the 5+132 subfactors.We then consider a planar subalgebra of the ‘group planar algebra’ which is naturally associated with a group Θ of automorphisms of the given group G. We show that this planar algebra corresponds to the ‘subgroup-subfactor’ associated with the inclusion Θ⊂(G⋊Θ) (given by the semi-direct product extension). We conclude with a discussion of the planar depth of this planar algebra PΘ in some examples
Lie Group Structures on Quotient Groups and Universal Complexifications for Infinite-Dimensional Lie Groups

AbstractWe characterize the existence of Lie group structures on quotient groups and the existence of universal complexifications for the class of Baker–Campbell–Hausdorff (BCH–) Lie groups, which subsumes all Banach–Lie groups and “linear” direct limit Lie groups, as well as the mapping groups CKr(M,G)≔{γ∈Cr(M,G) : γ∣M\K=1}, for every BCH–Lie group G, second countable finite-dimensional smooth manifold M, compact subset K of M, and 0⩽r⩽∞. Also the corresponding test function groups Dr(M,G)=⋃KCKr(M,G) are BCH–Lie groups
The Integrated Density of States for Some Random Operators with Nonsign Definite Potentials

AbstractWe study the integrated density of states of random Anderson-type additive and multiplicative perturbations of deterministic background operators for which the single-site potential does not have a fixed sign. Our main result states that, under a suitable assumption on the regularity of the random variables, the integrated density of states of such random operators is locally Hölder continuous at energies below the bottom of the essential spectrum of the background operator for any nonzero disorder, and at energies in the unperturbed spectral gaps, provided the randomness is sufficiently small. The result is based on a proof of a Wegner estimate with the correct volume dependence. The proof relies upon the Lp-theory of the spectral shift function for p⩾1 (Comm. Math. Phys.218 (2001), 113–130), and the vector field methods of Klopp (Comm. Math. Phys.167 (1995), 553–569). We discuss the application of this result to Schrödinger operators with random magnetic fields and to band-edge localization
The Fine Structure of the Kasparov Groups II: Topologizing the UCT

AbstractThe Kasparov groups KK*(A,B) have a natural structure as pseudopolonais groups. In this paper we analyze how this topology interacts with the terms of the Universal Coefficient Theorem (UCT) and the splittings of the UCT constructed by Rosenberg and the author, as well as its canonical three term decomposition which exists under bootstrap hypotheses. We show that the various topologies on ExtZ1(K*(A),K*(B)) and other related groups mostly coincide. Then we focus attention on the Milnor sequence and the fine structure subgroup of KK*(A,B). An important consequence of our work is that under bootstrap hypotheses the closure of zero of KK*(A,B) is isomorphic to the group PextZ1(K*(A),K*(B)). Finally, we introduce new splitting obstructions for the Milnor and Jensen sequences and prove that these sequences split if K*(A) or K*(B) is torsion-free
Description of the Automorphism Group Aut(A/Aα) for a Minimal Action of a Compact Kac Algebra and Its Application

AbstractIt is shown that, for a minimal action α of a compact Kac algebra K on a factor A, the group of all automorphisms leaving the fixed-point algebra Aα pointwise invariant is topologically isomorphic to the intrinsic group of the dual Kac algebra K̂. As an application, in the case where dim K<,∞, the left (in fact, two-sided) coideal of K determined by the normalizer (group) of Aα in A through the Izumi–Longo–Popa (Galois) correspondence is identified. As a consequence, we prove that, when A is the AFD II1 factor, K is cocommutative if and only if Aα⊆A contains a common Cartan subalgebra. This result is an extension of a result due to Jones and Popa
Non-Commutative Martingale Transforms

AbstractWe prove that non-commutative martingale transforms are of weak type (1,1). More precisely, there is an absolute constant C such that if M is a semi-finite von Neumann algebra and (Mn)n=1∞ is an increasing filtration of von Neumann subalgebras of M then for any non-commutative martingale x=(xn)n=1∞ in L1(M), adapted to (Mn)n=1∞, and any sequence of signs (εn)n=1∞,∥ε1x1+∑n=2Nεn(xn−xn−1)∥1,∞⩽C∥xN∥1 for every N⩾2. This generalizes a result of Burkholder from classical martingale theory to non-commutative setting and answers positively a question of Pisier and Xu. As applications, we get the optimal order of the unconditional Martingale differences (UMD)-constants of the Schatten class Sp when p→∞. Similarly, we prove that the UMD-constant of the finite-dimensional Schatten class Sn1 is of order log(n+1). We also discuss the Pisier–Xu non-commutative Burkholder–Gundy inequalities
Matrix Finite-Zone Dirac-Type Equations

AbstractWeyl–Titchmarsh matrix functions play an essential role in the spectral theory of Dirac-type equations (Oper. Theory: Adv. Appl.107 (1999)). In this paper, we have constructed a class of Weyl–Titchmarsh matrix-functions generating potentials of finite-zone type. It has turned out that the corresponding potentials have derivatives of an arbitrary order. Using the above-mentioned results, we deduce the matrix analogue of the trace formula for finite-zone matrix potentials. In the last part of the paper, we consider separately the scalar case of Dirac-type equations. For this case, we have constructed finite-zone potentials in explicit forms and proved that these potentials are quasiperiodical. We note that for scalar Schrödinger equations the corresponding results are well known (see Invent. Math.30 (1975), 217–274; “Soliton and the Inverse Scattering Transform,” SIAM, Philadelphia, 1981; Rev. Sci. Technol.23 (1983), 20–50; “Theory of Solitons, The Method of Inverse Problem,” New York, 1984; “Inverse Sturm–Liouville Problems,” VSP, Zeist, 1987; “Inverse Spectral Theory,” Academic Press, New York, 1987)
Branching Coefficients of Holomorphic Representations and Segal–Bargmann Transform

AbstractLet D=G/K be a complex bounded symmetric domain of tube type in a Jordan algebra VC, and let D=H/L=D∩V be its real form in a Jordan algebra V⊂VC. The analytic continuation of the holomorphic discrete series on Dopf; forms a family of interesting representations of G. We consider the restriction on D and the branching rule under H of the scalar holomorphic representations. The unitary part of the restriction map gives then a generalization of the Segal–Bargmann transform. The group L is a spherical subgroup of K and we find a canonical basis of L-invariant polynomials in the components of the Schmid decomposition and we express them in terms of the Jack symmetric polynomials. We prove that the Segal–Bargmann transform of those L-invariant polynomials are, under the spherical transform on D, multi-variable Wilson-type polynomials and we give a simple alternative proof of their orthogonality relation. We find the expansion of the spherical functions on D, when extended to a holomorphic function in a neighborhood of 0∈D, in terms of the L-spherical holomorphic polynomials on D, the coefficients being the Wilson polynomials
Spectral Synthesis and Topologies on Ideal Spaces for Banach*-Algebras

AbstractThis paper continues the study of spectral synthesis and the topologies τ∞ and τr on the ideal space of a Banach algebra, concentrating on the class of Banach *-algebras, and in particular on L1-group algebras. It is shown that if a group G is a finite extension of an abelian group then τr is Hausdorff on the ideal space of L1(G) if and only if L1(G) has spectral synthesis, which in turn is equivalent to G being compact. The result is applied to nilpotent groups, [FD]−-groups, and Moore groups. An example is given of a non-compact, non-abelian group G for which L1(G) has spectral synthesis. It is also shown that if G is a non-discrete group then τr is not Hausdorff on the ideal lattice of the Fourier algebra A(G)
Some Remarks on Operator-Norm Convergence of the Trotter Product Formula on Banach Spaces

AbstractWe extend the Trotter–Kato–Chernoff theory of strong approximation of C0 semigroups on Banach spaces to operator-norm approximation of analytic semigroups with error estimate. As application we obtain a criterion for the operator-norm convergence of the Trotter product formula on Banach spaces with error estimate n−1 log n, provided one of the generators has a bounded H∞ functional calculus. For both results, we present versions for approximation in operator-ideal-norms such as the trace norm or the Hilbert–Schmidt norm. Finally, we give some remarks on the operator-norm convergence of the Trotter product formula for semigroups acting on a scale of Lp-spaces
Ergodic Theory and Maximal Abelian Subalgebras of the Hyperfinite Factor

AbstractLet T be a free ergodic measure-preserving action of an abelian group G on (X,μ). The crossed product algebra RT=L∞(X,μ)⋊ G has two distinguished masas, the image CT of L∞(X,μ) and the algebra ST generated by the image of G. We conjecture that conjugacy of the singular masas ST(1) and ST(2) for weakly mixing actions T(1) and T(2) of different groups implies that the groups are isomorphic and the actions are conjugate with respect to this isomorphism. Our main result supporting this conjecture is that the conclusion is true under the additional assumption that the isomorphism γ : RT(1)→RT(2) such that γ(ST(1))=ST(2) has the property that the Cartan subalgebras γ(CT(1)) and CT(2) of RT(2) are inner conjugate. We discuss a stronger conjecture about the structure of the automorphism group Aut(RT,ST), and a weaker one about entropy as a conjugacy invariant. We study also the Pukanszky and some related invariants of ST, and show that they have a simple interpretation in terms of the spectral theory of the action T. It follows that essentially all values of the Pukanszky invariant are realized by the masas ST, and there exist non-conjugate singular masas with the same Pukanszky invariant
Functional Inequalities and Spectrum Estimates: The Infinite Measure Case

AbstractAs a continuation of [13] where a Poincaré-type inequality was introduced to study the essential spectrum on the L2-space of a probability measure, this paper provides a modification of this inequality so that the infimum of the essential spectrum is well described even if the reference measure is infinite. High-order eigenvalues as well as the corresponding semigroup are estimated by using this new inequality. Criteria of the inequality and estimates of the inequality constants are presented. Finally, some concrete examples are considered to illustrate the main results. In particular, estimates of high-order eigenvalues obtained in this paper are sharp as checked by two examples on the Euclidean space
Fonctions D(G/H)-Finies sur un Espace Symétrique Réductif

AbstractIt is well known that, on Rn, every smooth function annihilated by a finite codimensional ideal in the algebra of constant coefficient differential operators, is a linear combination of polynomial exponential functions, P(x)eλ(x), λ ∈ Hom(Rn,C). Furthermore, the polynomial functions are obtained by applying to the exponential functions eλ(x) some constant coefficient differential operator in the parameter λ. We generalize this fact to the reductive symmetric spaces' case, the role of the exponential functions being taken by the Eisenstein integrals
Intraseasonal characterization of glass eel migration in the River Tiber: Space and time dynamics

Glass eel (Anguilla anguilla) upstream migration was studied in the River Tiber estuary to obtain a better understanding of spatial and temporal migration dynamics within the season of ascent. Using data from glass eel fisheries, time series analysis of daily catches per unit of effort revealed a fortnightly cycle that can be related to invasion waves possibly corresponding to tidal currents. The amplitude of these waves appeared to correspond to the tidal area of the estuary. Furthermore, glass eels apparently had a delay in this area before resuming upstream migration. (C) 1995 The Fisheries Society of the British Isle
Acclimation trials of juvenile Italian sturgeon to different salinities: Morpho-physiological descriptors

In this study the first experimental trials of acclimation to salinities of the Italian sturgeon Acipenser naccarii are described. Preliminary observations regarding some morphological features of the gut, kidney and gills following exposure to 20 and 30% salinity are reported, and compared with those displayed by many teleosts in hyper- and hypoosmoregulation. Results are discussed with regard to the osmoregulatory mechanisms and to the physiological limits of adaptability of this species in the second year of its life cycle. Within the Acipenseridae, Acipenser naccarii is generally considered a euryhaline species, but nothing is known about its mechanisms of osmotic homeostasis. This species could be a good candidate for aquaculture in fresh and brackish waters owing to the recent success obtained in artificial reproduction
Computational Simulation of Dynamic Stall on the NLR 7301 Airfoil

The article of record as published may be found at http://dx.doi.org/10.1006/jfls.2000.0299The dynamic stall behavior of the supercritical NLR 7301 airfoil is analyzed with a 2-D
thin-layer Navier-Stokes code. The code solves the compressible Reynolds-averaged Navier-
Stokes equations with an upwind biased numerical scheme in combination with the
Baldwin}Lomax or the Baldwin}Barth turbulence models. The effect of boundary layer
transition is incorporated using the transition length model of Gostelow et al. The transition
onset location is determined with Michel's formula or it can be specified as an input parameter.
The two turbulence models yield significantly different steady-state lift coefficients at incidences
greater than 8 degrees. The use of the one-equation Baldwin}Barth model together with the Gostelow
transition model is found to give substantially better agreement with the experimental data of
McCroskey et al. than the Baldwin}Lomax model. Also, the unsteady computations are
strongly affected by the choice of the turbulence model. The Baldwin}Barth model predicts
the lift hysteresis loops consistently better than the algebraic turbulence model. However, the
one-equation model improves the prediction of the moment hysteresis loops only for one test
case.Deutsche Forschungsgemeinschaft (DFG)Naval Postgraduate SchoolDeutsche Forschungsgemeinschaft (DFG)Naval Postgraduate Schoo
On the Force Decompositions of Lighthill and Morison

The article of record as published may be located at http://dx.doi.org/10.1006/jfls.2000.0342Lighthill's assertion that the viscous drag force and the inviscid inertia force acting on a bluff body immersed in a time-dependent flow operate independently is not in conformity with the existing exact solutions and experimental facts. The two force components are interdependent as well as dependent on the parameters characterizing the phenomenon: the rate of diffusion of vorticity, relative amplitude of the oscillation, and the surface
roughness
Nonlinear synchronization in open flows

International audienceThe selection criteria governing finite-amplitude synchronized oscillating states are discussed for model systems and real wake flows in a domain of infinite streamwise extent. Two types of nonlinear global modes are possible: hat modes with overall smoothly varying amplitude and elephant modes with a sharp front. The vortex street in wake flows is of elephant type, as observed in direct numerical simulations of a real spatially developing wake. Furthermore, the elephant frequency selection criterion is in excellent agreement with the numerically determined vortex shedding frequency