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Function Spaces of Logarithmic Smoothness: Embeddings and Characterizations
In this paper we present a comprehensive treatment of function spaces with logarithmic smoothness (Besov, Sobolev, Triebel-Lizorkin).
We establish the following results:
The key tools behind our results
are limiting interpolation techniques and new characterizations of Besov and Sobolev norms in terms of the behavior of the Fourier
transforms for functions such that their Fourier transforms are of monotone type or lacunary series.
eBook
Functional Analysis, Harmonic Analysis, and Image Processing
This volume is dedicated to the memory of Björn Jawerth. It contains original research contributions and surveys in several of the areas of mathematics to which Björn made important contributions. Those areas include harmonic analysis, image processing, and functional analysis, which are of course interrelated in many significant and productive ways.Among the contributors are some of the world's leading experts in these areas. With its combination of research papers and surveys, this book may become an important reference and research tool.This book should be of interest to advanced graduate students and professional researchers in the areas of functional analysis, harmonic analysis, image processing, and approximation theory. It combines articles presenting new research with insightful surveys written by foremost experts.
eBook
Recent trends in operator theory and applications: Workshop on Recent Trends in Operator Theory and Applications, May 3-5, 2018, the University of Memphis, Memphis, Tennessee
This volume contains the proceedings of the workshop on Recent Trends in Operator Theory and Applications (RTOTA 2018), held from May 3-5, 2018, at the University of Memphis, Memphis, Tennessee.The articles introduce topics from operator theory to graduate students and early career researchers. Each such article provides insightful references, selection of results with articulation to modern research and recent advances in the area.Topics addressed in this volume include: generalized numerical ranges and their application to study perturbation of operators, and connections to quantum error correction; a survey of results on Toeplitz operators, and applications of Toeplitz operators to the study of reproducing kernel functions; results on the 2-local reflexivity problem of a set of operators; topics from the theory of preservers; and recent trends on the study of quotients of tensor product spaces and tensor operators. It also includes research articles that present overviews of state-of-the-art techniques from operator theory as well as applications to recent research trends and open questions. A goal of all articles is to introduce topics within operator theory to the general public.
eBook
Recent Trends in Operator Theory and Applications
This volume contains the proceedings of the workshop on Recent Trends in Operator Theory and Applications (RTOTA 2018), held from May 3-5, 2018, at the University of Memphis, Memphis, Tennessee. The articles introduce topics from operator theory to graduate students and early career researchers. Each such article provides insightful references, selection of results with articulation to modern research and recent advances in the area. Topics addressed in this volume include: generalized numerical ranges and their application to study perturbation of operators, and connections to quantum error correction; a survey of results on Toeplitz operators, and applications of Toeplitz operators to the study of reproducing kernel functions; results on the 2-local reflexivity problem of a set of operators; topics from the theory of preservers; and recent trends on the study of quotients of tensor product spaces and tensor operators. It also includes research articles that present overviews of state-of-the-art techniques from operator theory as well as applications to recent research trends and open questions. A goal of all articles is to introduce topics within operator theory to the general public.
eBook
Functional Analysis and Geometry
This is the first of two volumes dedicated to the centennial of the distinguished mathematician Selim Grigorievich Krein. The companion volume is Contemporary Mathematics, Volume 734.Krein was a major contributor to functional analysis, operator theory, partial differential equations, fluid dynamics, and other areas, and the author of several influential monographs in these areas. He was a prolific teacher, graduating 83 Ph.D. students. Krein also created and ran, for many years, the annual Voronezh Winter Mathematical Schools, which significantly influenced mathematical life in the former Soviet Union.The articles contained in this volume are written by prominent mathematicians, former students and colleagues of Selim Krein, as well as lecturers and participants of Voronezh Winter Schools. They are devoted to a variety of contemporary problems in functional analysis, operator theory, several complex variables, topological dynamics, and algebraic, convex, and integral geometry.
eBook
Norm derivatives and characterizations of inner product spaces
The book provides a comprehensive overview of the characterizations of real normed spaces as inner product spaces based on norm derivatives and generalizations of the most basic geometrical properties of triangles in normed spaces. Since the appearance of Jordan-von Neumann's classical theorem (The Parallelogram Law) in 1935, the field of characterizations of inner product spaces has received a significant amount of attention in various literature texts. Moreover, the techniques arising in the theory of functional equations have shown to be extremely useful in solving key problems in the characterizations of Banach spaces as Hilbert spaces.
eBook
Function spaces in modern analysis : Sixth Conference on Function Spaces, May 18-22, 2010, Southern Illinois University, Edwardsville
This volume contains the proceedings of the Sixth Conference on Function Spaces, which was held from May 18-22, 2010, at Southern Illinois University at Edwardsville. The papers cover a broad range of topics, including spaces and algebras of analytic functions of one and of many variables (and operators on such spaces), spaces of integrable functions, spaces of Banach-valued functions, isometries of function spaces, geometry of Banach spaces, and other related subjects.
eBook
Geometry of normed linear spaces : proceedings of a conference held June 9-12, 1983, in honor of Mahlon Marsh Day
These 17 papers result from a 1983 conference held to honor Professor Mahlon Marsh Day upon his retirement from the University of Illinois. Each of the main speakers was invited to take some aspect of Day's pioneering work as a starting point: he was the first American mathematician to study normed spaces from a geometric standpoint and, for a number of years, pioneered American research on the structure of Banach spaces. The material is aimed at researchers and graduate students in functional analysis. Many of the articles are expository and are written for the reader with only a basic background in the theory of normed linear spaces.
eBook