05247nam 2200637Ia 450 991046480340332120200520144314.01-283-73939-9981-4407-01-1(CKB)3400000000087230(EBL)1069830(OCoLC)818848246(SSID)ssj0000913920(PQKBManifestationID)11551380(PQKBTitleCode)TC0000913920(PQKBWorkID)10862231(PQKB)10922501(MiAaPQ)EBC1069830(WSP)00002822(Au-PeEL)EBL1069830(CaPaEBR)ebr10622798(CaONFJC)MIL405189(EXLCZ)99340000000008723020121129d2013 uy 0engur|n|---|||||txtccrFunctional equations on hypergroups[electronic resource] /Laszlo SzekelyhidiSingapore World Scientific20131 online resource (210 p.)Description based upon print version of record.981-4407-00-3 Includes bibliographical references and index.Contents; Preface; 1. Introduction; 1.1 Basic concepts and facts; 1.2 Convolution of subsets; 1.3 Invariant means on hypergroups; 1.4 Haar measure on hypergroups; 1.5 Exponential functions on hypergroups; 1.6 Exponential families on hypergroups; 1.7 Additive and multi-additive functions on hypergroups; 1.8 Moment functions on hypergroups; 1.9 Exponentials and additive functions on a special hypergroup; 2. Polynomial hypergroups in one variable; 2.1 Polynomial hypergroups in one variable; 2.2 Exponential and additive functions on polynomial hypergroups2.3 Moment functions on polynomial hypergroups2.4 Moment functions on the SU(2)-hypergroup; 3. Polynomial hypergroups in several variables; 3.1 Polynomial hypergroups in several variables; 3.2 Exponential and additive functions on multivariate polynomial hypergroups; 3.3 Moment function sequences on multivariate polynomial hypergroups; 4. Sturm-Liouville hypergroups; 4.1 Sturm-Liouville functions; 4.2 Exponentials and additive functions on Sturm-Liouville hypergroups; 4.3 Moment functions on Sturm-Liouville hypergroups; 5. Two-point support hypergroups; 5.1 Conditional functional equations5.2 Two-point support hypergroups of noncompact type5.3 Moment functions on two-point support hypergroups of noncompact type; 5.4 Two-point support hypergroups of compact type; 5.5 The cosh hypergroup; 5.6 Associated pairs of moment functions; 6. Spectral analysis and synthesis on polynomial hypergroups; 6.1 Spectral analysis and spectral synthesis on hypergroups; 6.2 Basic concepts and facts; 6.3 Spectral analysis on polynomial hypergroups in a single variable; 6.4 Exponential polynomials on polynomial hypergroups in a single variable6.5 Spectral synthesis on polynomial hypergroups in a single variable6.6 Spectral analysis and spectral synthesis on multivariate polynomial hypergroups; 6.7 Spectral analysis and moment functions; 7. Spectral analysis and synthesis on Sturm-Liouville hypergroups; 7.1 Exponential monomials on Sturm-Liouville hypergroups; 7.2 Linear independence of special exponential monomials; 7.3 Spectral analysis on Sturm-Liouville hypergroups; 8. Moment problems on hypergroups; 8.1 The moment problem in general; 8.2 Uniqueness on polynomial hypergroups; 8.3 The case of Sturm-Liouville hypergroups8.4 An approximation result9. Special functional equations on hypergroups; 9.1 The sine functional equation on polynomial hypergroups; 9.2 The cosine functional equation on polynomial hypergroups; 9.3 The Levi-Civita functional equation; 10. Difference equations on polynomial hypergroups; 10.1 Introduction; 10.2 Difference equations with 1-translation; 10.3 Difference equations with general translation; 11. Stability problems on hypergroups; 11.1 Stability of exponential functions on hypergroups; 11.2 Stability of additive functions on hypergroups11.3 Superstability of a mixed-type functional equationThe theory of hypergroups is a rapidly developing area of mathematics due to its diverse applications in different areas like probability, harmonic analysis, etc. This book exhibits the use of functional equations and spectral synthesis in the theory of hypergroups. It also presents the fruitful consequences of this delicate "marriage" where the methods of spectral analysis and synthesis can provide an efficient tool in characterization problems of function classes on hypergroups.This book is written for the interested reader who has open eyes for both functional equations and hypergroups, andFunctional equationsInequalities (Mathematics)Electronic books.Functional equations.Inequalities (Mathematics)515.75Székelyhidi László982287MiAaPQMiAaPQMiAaPQBOOK9910464803403321Functional equations on hypergroups2242040UNINA