Functional analysis and transforms

This first volume of a two-volume overview covers the basic theory of Banach spaces, harmonic analysis and probability.

This volume discusses an in-depth theory of function spaces in an Euclidean setting, including several new features, not previously covered in the literature.

This book contains the contributions resulting from the 6th Italian-Japanese workshop on Geometric Properties for Parabolic and Elliptic PDEs, which was held in Cortona (Italy) during the week of May 20-24, 2019.

Special functions are pervasive in all fields of science and industry.

When first published in 1959, this book was the basis of a two-semester course in complex analysis for upper undergraduate and graduate students.

Fourier analysis has been the inspiration for a technological wave of advances in fields such as imaging processing, financial modeling, algorithms and sequence design.

Asymptotic Geometric Analysis is concerned with the geometric and linear properties of finite dimensional objects, normed spaces, and convex bodies, especially with the asymptotics of their various quantitative parameters as the dimension tends to infinity.

This volume is part of the collaboration agreement between Springer and the ISAAC society.

This textbook provides a graduate-level introduction to the spectral theory of linear operators on Banach and Hilbert spaces, guiding readers through key components of spectral theory and its applications in quantum physics.

For more than forty years, the equation y'(t) = Ay(t) + u(t) in Banach spaces has been used as model for optimal control processes described by partial differential equations, in particular heat and diffusion processes.

This textbook introduces spectral theory for bounded linear operators by focusing on (i) the spectral theory and functional calculus for normal operators acting on Hilbert spaces; (ii) the Riesz-Dunford functional calculus for Banach-space operators; and (iii) the Fredholm theory in both Banach and Hilbert spaces.

This textbook offers an extensive list of completely solved problems in mathematical analysis.

Fractional equations and models play an essential part in the description of anomalous dynamics in complex systems.

This book concerns matrix and operator equations that are widely applied in various disciplines of science to formulate challenging problems and solve them in a faithful way.

The chapters in this volume are based on talks given at the inaugural Aspects of Time-Frequency Analysis conference held in Turin, Italy from July 5-7, 2017, which brought together experts in harmonic analysis and its applications.

Building on the foundation laid in the first volume of Subharmonic Functions, which has become a classic, this second volume deals extensively with applications to functions of a complex variable.

This 3rd edition provides an insight into the mathematical crossroads formed by functional analysis (the macroscopic approach), partial differential equations (the mesoscopic approach) and probability (the microscopic approach) via the mathematics needed for the hard parts of Markov processes.

This volume opens the world of free probability to a wide variety of readers.

This book is an introduction to methods for solving partial differential equations (PDEs).

This book deals with elliptic differential equations, providing the analytic background necessary for the treatment of associated spectral questions, and covering important topics previously scattered throughout the literature.

Tutorial survey papers on important areas of ergodic theory, with related research papers.

A guide to the new research in the field of fractional order analysis Fractional Order Analysis contains the most recent research findings in fractional order analysis and its applications.

This textbook offers a concise introduction to spectral theory, designed for newcomers to functional analysis.

The book collects chapters on operator theory as well as related approximation results and analytic inequalities.

Number Theory: Tradition and Modernization is a collection of survey and research papers on various topics in number theory.

A thorough graduate-level introduction to the variational analysis of nonlinear problems described by nonlocal operators.

At the intersection of mathematics, engineering, and computer science sits the thriving field of compressive sensing.

A sweeping exploration of the development and far-reaching applications of harmonic analysis such as signal processing, digital music, Fourier optics, radio astronomy, crystallography, medical imaging, spectroscopy, and more.

This book presents a thorough discussion of the theory of abstract inverse linear problems on Hilbert space.

This fully revised, updated, and corrected edition of The Elements of Operator Theory includes a significant expansion of problems and solutions used to illustrate the principles of operator theory.

The seminar on Stochastic Analysis and Mathematical Physics started in 1984 at the Catholic University of Chile in Santiago and has been an on- going research activity.

Körner provides a shop-window for some of the ideas, techniques and elegant results of Fourier analysis.

This second edition of Generalized Functions has been strengthened in many ways.

This book is aimed toward graduate students and researchers in mathematics, physics and engineering interested in the latest developments in analytic inequalities, Hilbert-Type and Hardy-Type integral inequalities, and their applications.

Functional Equations and Inequalities with Applications presents a comprehensive, nearly encyclopedic, study of the classical topic of functional equations.

These volumes are companions to the treatise; "e;Fundamentals of the Theory of Operator Algebras,"e; which appeared as Volume 100 - I and II in the series, Pure and Applied Mathematics, published by Academic Press in 1983 and 1986, respectively.

Representations, Wavelets, and Frames contains chapters pertaining to this theme from experts and expositors of renown in mathematical analysis and representation theory.

This is a problem book on Hilbert space operators (Le.

An introduction to the theory of operator spaces, emphasising applications to C*-algebras.

For the past several decades, the study of free boundary problems has been a very active subject of research occurring in a variety of applied sciences.

This book presents the proceedings of the international conference Particle Systems and Partial Differential Equations X, which was held at the University of Minho, Braga, Portugal, from 2022.

Boundary value problems which have variational expressions in form of inequal- ities can be divided into two main classes.

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The isomonodromic deformation equations such as the Painleve and Garnier systems are an important class of nonlinear differential equations in mathematics and mathematical physics.

The aim of this work is to present, in a unified and reasonably self-contained way, certain aspects of functional analysis which are needed to treat function spaces whose topology is not derived from a single norm, their topological duals and operators between those spaces.