Mathematical analysis and applications : selected topics / edited by Michael Ruzhansky, Hemen Dutta, Ravi P. Agarwal.

Contributor(s):

Material type: Text

TextPublisher: Hoboken, NJ : John Wiley & Sons, Inc., [2018]Description: 1 online resourceContent type:

text

Media type:

computer

Carrier type:

online resource

ISBN:

9781119414308
111941430X

Subject(s):

Genre/Form:

Electronic books.

Additional physical formats: Print version:: Mathematical analysis and applications.DDC classification:

515 23

LOC classification:

QA300 .M225 2018

Online resources:

Wiley Online Library

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 FussCatalan 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 CatalanQi Function 111 5.2.1 The Fuss Numbers 111 5.2.2 A Definition of the CatalanQi Function 111 5.2.3 Some Identities of the CatalanQi Function 112 5.2.4 Integral Representations of the CatalanQi Function 114 5.2.5 Asymptotic Expansions of the CatalanQi Function 115 5.2.6 Complete Monotonicity of the CatalanQi Function 116 5.2.7 Schur-Convexity of the CatalanQi Function 118 5.2.8 Generating Functions of the CatalanQi Numbers 118 5.2.9 A Double Inequality of the CatalanQi Function 118 5.2.10 The q-CatalanQi 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 FussCatalan Numbers 119 5.3.1 A Definition of the FussCatalan Numbers 119 5.3.2 A Product-Ratio Expression of the FussCatalan Numbers 120 5.3.3 Complete Monotonicity of the FussCatalan Numbers 120 5.3.4 A Double Inequality for the FussCatalan Numbers 121 5.4 The FussCatalanQi Function 121 5.4.1 A Definition of the FussCatalanQi Function 121 5.4.2 A Product-Ratio Expression of the FussCatalanQi Function 122 5.4.3 Integral Representations of the FussCatalanQi Function 123 5.4.4 Complete Monotonicity of the FussCatalanQi 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 UlamHyers Stabilities of EulerLagrangeJensen General (a, b; k = <

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Mathematical analysis and applications : selected topics / edited by Michael Ruzhansky, Hemen Dutta, Ravi P. Agarwal.

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