Mathematical analysis and applications : selected topics /: selected topics. (2018)

• Record Type: Book
• Further Information: Note: Edited by Michael Ruzhansky, Hemen Dutta, Ravi P. Agarwal.
• Editors: Ruzhansky, M (Michael); Dutta, Hemen, 1981-; Agarwal, Ravi P
• 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-BodyWave Scattering Problems for Small Scatterers and CreatingMaterials with a Desired Refraction Coefficient 57; Alexander G. Ramm 3.1 Introduction 57 3.2 Derivation of the Formulas for One-BodyWave 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 andWedad Saleh 4.1 Brief Introduction 77 4.2 Generalized E-Convex Functions 78 4.3 E �� -Epigraph 84 4.4 Generalized s -Convex Functions 85 4.5 Applications to Special Means 96 References 98 5 Some Properties and Generalizations of the Catalan, Fuss, and Fuss–Catalan Numbers 101; Feng Qi and Bai-Ni Guo 5.1 The Catalan Numbers 101 5.1.1 A Definition of the Catalan Numbers 101 5.1.2 The History of the Catalan Numbers 101 5.1.3 A Generating Function of the Catalan Numbers 102 5.1.4 Some Expressions of the Catalan Numbers 102 5.1.5 Integral Representations of the Catalan Numbers 103 5.1.6 Asymptotic Expansions of the Catalan Function 104 5.1.7 Complete Monotonicity of the Catalan Numbers 105 5.1.8 Inequalities of the Catalan Numbers and Function 106 5.1.9 The Bell Polynomials of the Second Kind and the Bessel Polynomials 109 5.2 The Catalan–Qi Function 111 5.2.1 The Fuss Numbers 111 5.2.2 A Definition of the Catalan–Qi Function 111 5.2.3 Some Identities of the Catalan–Qi Function 112 5.2.4 Integral Representations of the Catalan–Qi Function 114 5.2.5 Asymptotic Expansions of the Catalan–Qi Function 115 5.2.6 Complete Monotonicity of the Catalan–Qi Function 116 5.2.7 Schur-Convexity of the Catalan–Qi Function 118 5.2.8 Generating Functions of the Catalan–Qi Numbers 118 5.2.9 A Double Inequality of the Catalan–Qi Function 118 5.2.10 The q -Catalan–Qi Numbers and Properties 119 5.2.11 The Catalan Numbers and the k -Gamma and k -Beta Functions 119 5.2.12 Series Identities Involving the Catalan Numbers 119 5.3 The Fuss–Catalan Numbers 119 5.3.1 A Definition of the Fuss–Catalan Numbers 119 5.3.2 A Product-Ratio Expression of the Fuss–Catalan Numbers 120 5.3.3 Complete Monotonicity of the Fuss–Catalan Numbers 120 5.3.4 A Double Inequality for the Fuss–Catalan Numbers 121 5.4 The Fuss–Catalan–Qi Function 121 5.4.1 A Definition of the Fuss–Catalan–Qi Function 121 5.4.2 A Product-Ratio Expression of the Fuss–Catalan–Qi Function 122 5.4.3 Integral Representations of the Fuss–Catalan–Qi Function 123 5.4.4 Complete Monotonicity of the Fuss–Catalan–Qi Function 124 5.5 Some Properties for Ratios of Two Gamma Functions 124 5.5.1 An Integral Representation and Complete Monotonicity 125 5.5.2 An Exponential Expansion for the Ratio of Two Gamma Functions 125 5.5.3 A Double Inequality for the Ratio of Two Gamma Functions 125 5.6 Some NewResults on the Catalan Numbers 126 5.7 Open Problems 126 Acknowledgments 127 References 127 6 Trace Inequalities of Jensen Type for Self-adjoint Operators in Hilbert Spaces: A Survey of Recent Results 135; Silvestru Sever Dragomir 6.1 Introduction 135 6.1.1 Jensen’s Inequality 135 6.1.2 Traces for Operators in Hilbert Spaces 138 6.2 Jensen’s Type Trace Inequalities 141 6.2.1 Some Trace Inequalities for Convex Functions 141 6.2.2 Some Functional Properties 145 6.2.3 Some Examples 151 6.2.4 More Inequalities for Convex Functions 154 6.3 Reverses of Jensen’s Trace Inequality 157 6.3.1 A Reverse of Jensen’s Inequality 157 6.3.2 Some Examples 163 6.3.3 Further Reverse Inequalities for Convex Functions 165 6.3.4 Some Examples 169 6.3.5 Reverses of Hölder’s Inequality 174 6.4 Slater’s Type Trace Inequalities 177 6.4.1 Slater’s Type Inequalities 177 6.4.2 Further Reverses 180 References 188 7 Spectral Synthesis and Its Applications 193; László Székelyhidi 7.1 Introduction 193 7.2 Basic Concepts and Function Classes 195 7.3 Discrete Spectral Synthesis 203 7.4 Nondiscrete Spectral Synthesis 217 7.5 Spherical Spectral Synthesis 219 7.6 Spectral Synthesis on Hypergroups 238 7.7 Applications 248 Acknowledgments 252 References 252 8 Various Ulam–Hyers Stabilities of Euler–Lagrange–Jensen General ( a, b ; k = <
• Edition: 1st
• Publisher Details: Hoboken, New Jersey : John Wiley & Sons, Inc
• Publication Date: 2018
• Extent: 1 online resource
• Subjects: 515; Mathematical analysis
• Languages: English
• ISBNs: 9781119414339; 9781119414308
• Related ISBNs: 9781119414346
• Notes: Note: Includes bibliographical references and index.; Note: Description based on CIP data; resource not viewed.
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