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An authoritative text that presents the current problems, theories, and applications of mathematical analysis research Mathematical Analysis and Applications : Selected Topics offers the theories, methods, and applications of a variety of targeted topics including: operator theory, approximation theory, fixed point theory, stability theory, minimization problems, many-body wave scattering problems, Basel problem, Corona problem, inequalities, generalized normed spaces, variations of functions and sequences, analytic generalizations of the Catalan, Fuss, and Fuss-Catalan Numbers, asymptotically developable functions, convex functions, Gaussian processes, image analysis, and spectral analysis and spectral synthesis. The authors--a noted team of international researchers in the field--highlight the basic developments for each topic presented and explore the most recent advances made in their area of study. The text is presented in such a way that enables the reader to follow subsequent studies in a burgeoning field of research. This important text: Presents a wide-range of important topics having current research importance and interdisciplinary applications such as game theory, image processing, creation of materials with a desired refraction coefficient, etc. Contains chapters written by a group of esteemed researchers in mathematical analysis Includes problems and research questions in order to enhance understanding of the information provided Offers references that help readers advance to further study Written for researchers, graduate students, educators, and practitioners with an interest in mathematical analysis, Mathematical Analysis and Applications : Selected Topic s includes the most recent research from a range of mathematical fields.

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An authoritative text that presents the current problems, theories, and applications of mathematical analysis research Mathematical Analysis and Applications : Selected Topics offers the theories, methods, and applications of a variety of targeted topics including: operator theory, approximation theory, fixed point theory, stability theory, minimization problems, many-body wave scattering problems, Basel problem, Corona problem, inequalities, generalized normed spaces, variations of functions and sequences, analytic generalizations of the Catalan, Fuss, and Fuss-Catalan Numbers, asymptotically developable functions, convex functions, Gaussian processes, image analysis, and spectral analysis and spectral synthesis. The authors--a noted team of international researchers in the field--highlight the basic developments for each topic presented and explore the most recent advances made in their area of study. The text is presented in such a way that enables the reader to follow subsequent studies in a burgeoning field of research. This important text: Presents a wide-range of important topics having current research importance and interdisciplinary applications such as game theory, image processing, creation of materials with a desired refraction coefficient, etc. Contains chapters written by a group of esteemed researchers in mathematical analysis Includes problems and research questions in order to enhance understanding of the information provided Offers references that help readers advance to further study Written for researchers, graduate students, educators, and practitioners with an interest in mathematical analysis, Mathematical Analysis and Applications : Selected Topic s includes the most recent research from a range of mathematical fields.

Table of Contents

Preface xv About the Editors xxi List of Contributors xxiii 1 Spaces of Asymptotically Developable Functions and Applications 1
Sergio Alejandro Carrillo Torres and Jorge Mozo Fernández 1.1 Introduction and Some Notations 1 1.2 Strong Asymptotic Expansions 2 1.3 Monomial Asymptotic Expansions 7 1.4 Monomial Summability for Singularly Perturbed Differential Equations 13 1.5 Pfaffian Systems 15 References 19 2 Duality for Gaussian Processes from Random Signed Measures 23
Palle E.T. Jorgensen and Feng Tian 2.1 Introduction 23 2.2 Reproducing Kernel Hilbert Spaces (RKHSs) in the Measurable Category 24 2.3 Applications to Gaussian Processes 30 2.4 Choice of Probability Space 34 2.5 A Duality 37 2.A Stochastic Processes 40 2.B Overview of Applications of RKHSs 45 Acknowledgments 50 References 51 3 Many-Body Wave Scattering Problems for Small Scatterers and Creating Materials with a Desired Refraction Coefficient 57
Alexander G. Ramm 3.1 Introduction 57 3.2 Derivation of the Formulas for One-Body Wave Scattering Problems 62 3.3 Many-Body Scattering Problem 65 3.3.1 The Case of Acoustically Soft Particles 68 3.3.2 Wave Scattering by Many Impedance Particles 70 3.4 Creating Materials with a Desired Refraction Coefficient 71 3.5 Scattering by Small Particles Embedded in an Inhomogeneous Medium 72 3.6 Conclusions 72 References 73 4 Generalized Convex Functions and their Applications 77
Adem Kiliçman and Wedad Saleh 4.1 Brief Introduction 77 4.2 Generalized E-Convex Functions 78 4.3 E

Long Description

An authoritative text that presents the current problems, theories, and applications of mathematical analysis research Mathematical Analysis and Applications : Selected Topics offers the theories, methods, and applications of a variety of targeted topics including: operator theory, approximation theory, fixed point theory, stability theory, minimization problems, many-body wave scattering problems, Basel problem, Corona problem, inequalities, generalized normed spaces, variations of functions and sequences, analytic generalizations of the Catalan, Fuss, and Fuss Catalan Numbers, asymptotically developable functions, convex functions, Gaussian processes, image analysis, and spectral analysis and spectral synthesis. The authors a noted team of international researchers in the field highlight the basic developments for each topic presented and explore the most recent advances made in their area of study. The text is presented in such a way that enables the reader to follow subsequent studies in a burgeoning field of research. This important text: Presents a wide-range of important topics having current research importance and interdisciplinary applications such as game theory, image processing, creation of materials with a desired refraction coefficient, etc. Contains chapters written by a group of esteemed researchers in mathematical analysis Includes problems and research questions in order to enhance understanding of the information provided Offers references that help readers advance to further study Written for researchers, graduate students, educators, and practitioners with an interest in mathematical analysis, Mathematical Analysis and Applications : Selected Topic s includes the most recent research from a range of mathematical fields.

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