Sharp Real Part Theorems

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Sharp Real Part Theorems

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Author : Gershon Kresin
language : en
Publisher: Springer
Release Date : 2007-03-05

Sharp Real Part Theorems written by Gershon Kresin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-03-05 with Mathematics categories.

This volume contains a coherent point of view on various sharp pointwise inequalities for analytic functions in a disk in terms of the real part of the function on the boundary circle or in the disk itself. Inequalities of this type are frequently used in the theory of entire functions and in the analytic number theory.

Complex Proofs Of Real Theorems

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Author : Peter D. Lax
language : en
Publisher: American Mathematical Soc.
Release Date : 2011-12-21

Complex Proofs Of Real Theorems written by Peter D. Lax and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-21 with Mathematics categories.

Complex Proofs of Real Theorems is an extended meditation on Hadamard's famous dictum, ``The shortest and best way between two truths of the real domain often passes through the imaginary one.'' Directed at an audience acquainted with analysis at the first year graduate level, it aims at illustrating how complex variables can be used to provide quick and efficient proofs of a wide variety of important results in such areas of analysis as approximation theory, operator theory, harmonic analysis, and complex dynamics. Topics discussed include weighted approximation on the line, Muntz's theorem, Toeplitz operators, Beurling's theorem on the invariant spaces of the shift operator, prediction theory, the Riesz convexity theorem, the Paley-Wiener theorem, the Titchmarsh convolution theorem, the Gleason-Kahane-Zelazko theorem, and the Fatou-Julia-Baker theorem. The discussion begins with the world's shortest proof of the fundamental theorem of algebra and concludes with Newman's almost effortless proof of the prime number theorem. Four brief appendices provide all necessary background in complex analysis beyond the standard first year graduate course. Lovers of analysis and beautiful proofs will read and reread this slim volume with pleasure and profit.

Analysis Partial Differential Equations And Applications

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Author : Alberto Cialdea
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-01-14

Analysis Partial Differential Equations And Applications written by Alberto Cialdea and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-14 with Mathematics categories.

This volume includes several invited lectures given at the International Workshop "Analysis, Partial Differential Equations and Applications", held at the Mathematical Department of Sapienza University of Rome, on the occasion of the 70th birthday of Vladimir G. Maz'ya, a renowned mathematician and one of the main experts in the field of pure and applied analysis. The book aims at spreading the seminal ideas of Maz'ya to a larger audience in faculties of sciences and engineering. In fact, all articles were inspired by previous works of Maz'ya in several frameworks, including classical and contemporary problems connected with boundary and initial value problems for elliptic, hyperbolic and parabolic operators, Schrödinger-type equations, mathematical theory of elasticity, potential theory, capacity, singular integral operators, p-Laplacians, functional analysis, and approximation theory. Maz'ya is author of more than 450 papers and 20 books. In his long career he obtained many astonishing and frequently cited results in the theory of harmonic potentials on non-smooth domains, potential and capacity theories, spaces of functions with bounded variation, maximum principle for higher-order elliptic equations, Sobolev multipliers, approximate approximations, etc. The topics included in this volume will be particularly useful to all researchers who are interested in achieving a deeper understanding of the large expertise of Vladimir Maz'ya.

Numerical Range Of Holomorphic Mappings And Applications

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Author : Mark Elin
language : en
Publisher: Springer
Release Date : 2019-03-11

Numerical Range Of Holomorphic Mappings And Applications written by Mark Elin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-11 with Mathematics categories.

This book describes recent developments as well as some classical results regarding holomorphic mappings. The book starts with a brief survey of the theory of semigroups of linear operators including the Hille-Yosida and the Lumer-Phillips theorems. The numerical range and the spectrum of closed densely defined linear operators are then discussed in more detail and an overview of ergodic theory is presented. The analytic extension of semigroups of linear operators is also discussed. The recent study of the numerical range of composition operators on the unit disk is mentioned. Then, the basic notions and facts in infinite dimensional holomorphy and hyperbolic geometry in Banach and Hilbert spaces are presented, L. A. Harris' theory of the numerical range of holomorphic mappings is generalized, and the main properties of the so-called quasi-dissipative mappings and their growth estimates are studied. In addition, geometric and quantitative analytic aspects of fixed point theory are discussed. A special chapter is devoted to applications of the numerical range to diverse geometric and analytic problems.

Banach Spaces And Descriptive Set Theory Selected Topics

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Author : Pandelis Dodos
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-05-10

Banach Spaces And Descriptive Set Theory Selected Topics written by Pandelis Dodos and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-10 with Mathematics categories.

This volume deals with problems in the structure theory of separable infinite-dimensional Banach spaces, with a central focus on universality problems. This topic goes back to the beginnings of the field and appears in Banach's classical monograph. The novelty of the approach lies in the fact that the answers to a number of basic questions are based on techniques from Descriptive Set Theory. Although the book is oriented on proofs of several structural theorems, in the main text readers will also find a detailed exposition of numerous “intermediate” results which are interesting in their own right and have proven to be useful in other areas of Functional Analysis. Moreover, several well-known results in the geometry of Banach spaces are presented from a modern perspective.

Enumerative Invariants In Algebraic Geometry And String Theory

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Author : Marcos Marino
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-08-22

Enumerative Invariants In Algebraic Geometry And String Theory written by Marcos Marino and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-22 with Mathematics categories.

Starting in the middle of the 80s, there has been a growing and fruitful interaction between algebraic geometry and certain areas of theoretical high-energy physics, especially the various versions of string theory. Physical heuristics have provided inspiration for new mathematical definitions (such as that of Gromov-Witten invariants) leading in turn to the solution of problems in enumerative geometry. Conversely, the availability of mathematically rigorous definitions and theorems has benefited the physics research by providing the required evidence in fields where experimental testing seems problematic. The aim of this volume, a result of the CIME Summer School held in Cetraro, Italy, in 2005, is to cover part of the most recent and interesting findings in this subject.

Harmonic Analysis And Partial Differential Equations

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Author : Anatoly Golberg
language : en
Publisher: Springer Nature
Release Date : 2023-03-25

Harmonic Analysis And Partial Differential Equations written by Anatoly Golberg and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-25 with Mathematics categories.

Over the course of his distinguished career, Vladimir Maz'ya has made a number of groundbreaking contributions to numerous areas of mathematics, including partial differential equations, function theory, and harmonic analysis. The chapters in this volume - compiled on the occasion of his 80th birthday - are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.

Generalized Bessel Functions Of The First Kind

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Author : Árpád Baricz
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-05-25

Generalized Bessel Functions Of The First Kind written by Árpád Baricz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-25 with Mathematics categories.

This volume studies the generalized Bessel functions of the first kind by using a number of classical and new findings in complex and classical analysis. It presents interesting geometric properties and functional inequalities for these generalized functions.

Complex Analysis And Dynamical Systems Vi

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Author : Lawrence Zalcman
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-05-19

Complex Analysis And Dynamical Systems Vi written by Lawrence Zalcman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-19 with Mathematics categories.

This volume contains the proceedings of the Sixth International Conference on Complex Analysis and Dynamical Systems, held from May 19–24, 2013, in Nahariya, Israel, in honor of David Shoikhet's sixtieth birthday. The papers range over a wide variety of topics in complex analysis, quasiconformal mappings, and complex dynamics. Taken together, the articles provide the reader with a panorama of activity in these areas, drawn by a number of leading figures in the field. They testify to the continued vitality of the interplay between classical and modern analysis. The companion volume (Contemporary Mathematics, Volume 653) is devoted to partial differential equations, differential geometry, and radon transforms.

Functional Differential Equations And Applications

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Author : Alexander Domoshnitsky
language : en
Publisher: Springer Nature
Release Date : 2022-02-02

Functional Differential Equations And Applications written by Alexander Domoshnitsky and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-02 with Mathematics categories.

This book discusses delay and integro-differential equations from the point of view of the theory of functional differential equations. This book is a collection of selected papers presented at the international conference of Functional Differential Equations and Applications (FDEA-2019), 7th in the series, held at Ariel University, Israel, from August 22–27, 2019. Topics covered in the book include classical properties of functional differential equations as oscillation/non-oscillation, representation of solutions, sign properties of Green's matrices, comparison of solutions, stability, control, analysis of boundary value problems, and applications. The primary audience for this book includes specialists on ordinary, partial and functional differential equations, engineers and doctors dealing with modeling, and researchers in areas of mathematics and engineering.