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Tightness, integral equicontinuity and compactness for evolution problems in Banach spaces

Riccarda Rossi, Giuseppe Savaré (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Compactness in the space L p ( 0 , T ; B ) , B being a separable Banach space, has been deeply investigated by J.P. Aubin (1963), J.L. Lions (1961, 1969), J. Simon (1987), and, more recently, by J.M. Rakotoson and R. Temam (2001), who have provided various criteria for relative compactness, which turn out to be crucial tools in the existence proof of solutions to several abstract time dependent problems related to evolutionary PDEs. In the present paper, the problem is examined in view of Young measure theory: exploiting...

Tightness of compact spaces is preserved by the t -equivalence relation

Oleg Okunev (2002)

Commentationes Mathematicae Universitatis Carolinae

We prove that if there is an open mapping from a subspace of C p ( X ) onto C p ( Y ) , then Y is a countable union of images of closed subspaces of finite powers of X under finite-valued upper semicontinuous mappings. This allows, in particular, to prove that if X and Y are t -equivalent compact spaces, then X and Y have the same tightness, and that, assuming 2 𝔱 > 𝔠 , if X and Y are t -equivalent compact spaces and X is sequential, then Y is sequential.

Time and space Sobolev regularity of solutions to homogeneous parabolic equations

Gabriella Di Blasio (1998)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We give necessary and sufficient conditions on the initial data such that the solutions of parabolic equations have a prescribed Sobolev regularity in time and space.

Toeplitz operators on Bergman spaces and Hardy multipliers

Wolfgang Lusky, Jari Taskinen (2011)

Studia Mathematica

We study Toeplitz operators T a with radial symbols in weighted Bergman spaces A μ p , 1 < p < ∞, on the disc. Using a decomposition of A μ p into finite-dimensional subspaces the operator T a can be considered as a coefficient multiplier. This leads to new results on boundedness of T a and also shows a connection with Hardy space multipliers. Using another method we also prove a necessary and sufficient condition for the boundedness of T a for a satisfying an assumption on the positivity of certain indefinite...

Toeplitz-Berezin quantization and non-commutative differential geometry

Harald Upmeier (1997)

Banach Center Publications

In this survey article we describe how the recent work in quantization in multi-variable complex geometry (domains of holomorphy, symmetric domains, tube domains, etc.) leads to interesting results and problems in C*-algebras which can be viewed as examples of the "non-commutative geometry" in the sense of A. Connes. At the same time, one obtains new functional calculi (of pseudodifferential type) with possible applications to partial differential equations and group representations.

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