Real analysis, real variables

Fourier Analysis and Boundary Value Problems provides a thorough examination of both the theory and applications of partial differential equations and the Fourier and Laplace methods for their solutions.

An excellent reference for anyone needing to examine properties of harmonic vector fields to help them solve research problems.

This book has two main objectives, the first of which is to extend the power of numerical Fourier analysis and to show by means of theoretical examples and numerous concrete applications that when computing discrete Fourier transforms of periodic and non periodic functions, the usual kernel matrix of the Fourier transform, the discrete Fourier transform (DFT), should be replaced by another kernel matrix, the eXtended Fourier transform (XFT), since the XFT matrix appears as a convergent quadrature of a more general transform, the fractional Fourier transform.

Motivated by recent increased activity of research on time scales, the book  provides a systematic approach to the study of the qualitative theory of boundedness, periodicity and stability of Volterra integro-dynamic equations on time scales.

Transmutation operators in differential equations and spectral theory can be used to reveal the relations between different problems, and often make it possible to transform difficult problems into easier ones.

This book presents eleven peer-reviewed papers from the 3rd International Conference on Applications of Mathematics and Informatics in Natural Sciences and Engineering (AMINSE2017) held in Tbilisi, Georgia in December 2017.

This textbook provides a thorough introduction to measure and integration theory, fundamental topics of advanced mathematical analysis.

This brief explores the Krasnosel'skii-Man (KM) iterative method, which has been extensively employed to find fixed points of nonlinear methods.

This book presents a compact and self-contained introduction to the theory of measure and integration.

This monograph offers a self-contained introduction to pseudodifferential operators and wavelets over real and p-adic fields.

Current research and applications in nonlinear analysis influenced by Haim Brezis and Louis Nirenberg are presented in this book by leading mathematicians.

This book develops the foundations of "e;summability calculus"e;, which is a comprehensive theory of fractional finite sums.

This book convenes a collection of carefully selected problems in mathematical analysis, crafted to achieve maximum synergy between analytic geometry and algebra and favoring mathematical creativity in contrast to mere repetitive techniques.

This textbook covers key topics of Elementary Calculus through selected exercises, in a sequence that facilitates development of problem-solving abilities and techniques.

This book is devoted to the study of certain integral representations for Neumann, Kapteyn, Schlomilch, Dini and Fourier series of Bessel and other special functions, such as Struve and von Lommel functions.

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

The main purpose of this book is to give a detailed and complete survey of recent progress related to the real-variable theory of Musielak-Orlicz Hardy-type function spaces, and to lay the foundations for further applications.

This textbook provides a gentle overview of fundamental concepts related to one-variable calculus.

This monograph uncovers the full capabilities of the Riemann integral.

This monograph is devoted to developing a theory of combined measure and shift invariance of time scales with the related applications to shift functions and dynamic equations.

This book covers the construction, analysis, and theory of continuous nowhere differentiable functions, comprehensively and accessibly.

This volume features recent development and techniques in evolution equations by renown experts in the field.

This book is about the rise and supposed fall of the mean value theorem.

This second edition provides a thorough introduction to contemporary convex function theory with many new results.

This book provides a  concise introduction to convex duality in financial mathematics.

Written by an expert on the topic and experienced lecturer, this textbook provides an elegant, self-contained introduction to functional analysis, including several advanced topics and applications to harmonic analysis.

This beginners' course provides students with a general and sufficiently easy to grasp theory of the Kurzweil-Henstock integral.

One of the main aims of this book is to exhibit some fruitful links between renewal theory and regular variation of functions.

This is a text that develops calculus 'from scratch', with complete rigorous arguments.

This book offers to the reader a self-contained treatment and systematic exposition of the real-valued theory of a nonabsolute integral on measure spaces.

This book deals with the development of Diophantine problems starting with Thue's path breaking result and culminating in Roth's theorem with applications.

This book serves as a textbook in real analysis.

This book is an introductory text on real analysis for undergraduate students.

This book discusses major topics in measure theory, Fourier transforms, complex analysis and algebraic topology.

This book provides a broad, interdisciplinary overview of non-Archimedean analysis and its applications.

Theories, methods and problems in approximation theory and analytic inequalities with a focus on differential and integral inequalities are analyzed in this book.

This book provides an in depth discussion of Loewner's theorem on the characterization of matrix monotone functions.

This compact textbook is a collection of the author's lecture notes for a two-semester graduate-level real analysis course.

This book sketches a path for newcomers into the theory of harmonic analysis on the real line.

The aim of this book is to present various facets of the theory and applications of Lipschitz functions, starting with classical and culminating with some recent results.

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.

This book presents a systematic treatment of generalized Orlicz spaces (also known as Musielak-Orlicz spaces) with minimal assumptions on the generating F-function.

An informative and useful account of complex numbers that includes historical anecdotes, ideas for further research, outlines of theory and a detailed analysis of the ever-elusory Riemann hypothesis.

Delta Functions has now been updated, restructured and modernised into a second edition, to answer specific difficulties typically found by students encountering delta functions for the first time.

Inequalities for Differential and Integral Equations has long been needed; it contains material which is hard to find in other books.