LEADER 05247nam 2200637Ia 450 001 9910464803403321 005 20200520144314.0 010 $a1-283-73939-9 010 $a981-4407-01-1 035 $a(CKB)3400000000087230 035 $a(EBL)1069830 035 $a(OCoLC)818848246 035 $a(SSID)ssj0000913920 035 $a(PQKBManifestationID)11551380 035 $a(PQKBTitleCode)TC0000913920 035 $a(PQKBWorkID)10862231 035 $a(PQKB)10922501 035 $a(MiAaPQ)EBC1069830 035 $a(WSP)00002822 035 $a(Au-PeEL)EBL1069830 035 $a(CaPaEBR)ebr10622798 035 $a(CaONFJC)MIL405189 035 $a(EXLCZ)993400000000087230 100 $a20121129d2013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aFunctional equations on hypergroups$b[electronic resource] /$fLaszlo Szekelyhidi 210 $aSingapore $cWorld Scientific$d2013 215 $a1 online resource (210 p.) 300 $aDescription based upon print version of record. 311 $a981-4407-00-3 320 $aIncludes bibliographical references and index. 327 $aContents; 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 hypergroups 327 $a2.3 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 equations 327 $a5.2 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 variable 327 $a6.5 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 hypergroups 327 $a8.4 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 hypergroups 327 $a11.3 Superstability of a mixed-type functional equation 330 $aThe 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, and 606 $aFunctional equations 606 $aInequalities (Mathematics) 608 $aElectronic books. 615 0$aFunctional equations. 615 0$aInequalities (Mathematics) 676 $a515.75 700 $aSze?kelyhidi$b La?szlo?$0982287 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910464803403321 996 $aFunctional equations on hypergroups$92242040 997 $aUNINA