LEADER 06073nam 22008295 450 001 9910437865603321 005 20251230060936.0 010 $a9783034805162 010 $a3034805160 024 7 $a10.1007/978-3-0348-0516-2 035 $a(CKB)2670000000342861 035 $a(EBL)1156185 035 $a(OCoLC)831115879 035 $a(SSID)ssj0000878409 035 $a(PQKBManifestationID)11469122 035 $a(PQKBTitleCode)TC0000878409 035 $a(PQKBWorkID)10836040 035 $a(PQKB)10109824 035 $a(DE-He213)978-3-0348-0516-2 035 $a(MiAaPQ)EBC1156185 035 $a(PPN)168307383 035 $a(MiFhGG)9783034805162 035 $a(EXLCZ)992670000000342861 100 $a20130130d2013 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAdvances in Harmonic Analysis and Operator Theory $eThe Stefan Samko Anniversary Volume /$fedited by Alexandre Almeida, Luís Castro, Frank-Olme Speck 205 $a1st ed. 2013. 210 1$aBasel :$cSpringer Basel :$cImprint: Birkhäuser,$d2013. 215 $a1 online resource (387 p.) 225 1 $aOperator Theory: Advances and Applications,$x2296-4878 ;$v229 300 $aDescription based upon print version of record. 311 08$a9783034807937 311 08$a3034807937 311 08$a9783034805155 311 08$a3034805152 327 $aAdvances in Harmonic Analysis and Operator Theory; The Stefan Samko Anniversary Volume; Contents; Preface; Stefan G. Samko - Mathematician, Teacher and Man; 1. Introduction; 2. Scientific origin from BVP and SIE, 1965-1974; 3. Research in Fractional Calculus (FC), 1967-1996; 3.1. One-dimensional Fractional Calculus; 3.1.1. Relations between left- and right-hand sided fractional integration; 3.1.2. Estimates of moduli of continuity; 3.1.3. In collaboration with Bertram Ross; 3.1.4. Other; 3.2. Multidimensional FC; 4. Equations with involutive operators, 1970-1977 327 $a5. Function spaces of fractional smoothness, influence of Steklov Mathematical Institute5.1. Hypersingular integrals and spaces of the type of Riesz potentials; 5.2. Potential type operators with homogeneous kernels; 5.3. Spherical HSI and potentials; 6. Portugal period; after 1995; 6.1. FC continued; constant exponents; 6.1.1. Approximative inverses for the fractional type operators; 6.1.2. Local nature of Riesz potential operators; 6.1.3. Miscellaneous; 6.2. Equations with involutive operators, continued; 6.3. Variable Exponent Analysis: 1993-2003 327 $a6.4. Variable Exponent Analysis in collaboration with V. Kokilashvili, 2001-present6.5. Variable Exponent Analysis, continued: 2004-present; 6.5.1. More on weighted estimates of potential operators; 6.5.2. Studies related to HSI and the range I?() (Lp()) in case of variable exponents; 6.5.3. Morrey and Campanato spaces; 6.5.4. PDO in variable exponent setting; 6.5.5. Miscellaneous in variable exponent analysis; 7. Miscellaneous; References; The Role of S.G. Samko in the Establishing and Development of the Theory of Fractional Differential Equations and Related Integral Operators 327 $a1. Main aspects of the modern theory of fractional differential equations1.1. Elements of the classification; Ordinary fractional differential equations; Fractional partial differential equations; 1.2. Methods of investigation; Treating problems:; Types of solutions:; Methods of solution:; 2. Basic components of investigations related to fractional differential equations; 2.1. Development of fractional calculus; 2.2. Development of the theory of first-order integral equations; 2.3. Development of methods of integral transforms; 2.4. Development of the theory of special functions 327 $a2.5. Development of multidimensional fractional calculus3. The role of Professor S.G. Samko in the creation and development of the theory of fractional differential equations; 3.1. Singular integral equations and boundary value problems; 3.2. Abel integral equations and their generalizations; 3.3. Integral equations with weak singularities; 3.4. Convolution type integral equations; 3.5. Fractional integro-differentiation; 3.6. Fractional powers of operators; 3.7. The theory of (one- and multidimensional) potential type operators; 4. Conclusion; Acknowledgment; References 327 $aEnergy Flow Above the Threshold of Tunnel Effect 330 $aThis volume is dedicated to Professor Stefan Samko on the occasion of his seventieth birthday. The contributions display the range of his scientific interests in harmonic analysis and operator theory. Particular attention is paid to fractional integrals and derivatives, singular, hypersingular and potential operators in variable exponent spaces, pseudodifferential operators in various modern function and distribution spaces, as well as related applications, to mention but a few. Most of the contributions were originally presented at two conferences in Lisbon and Aveiro, Portugal, in June?July 2011. 410 0$aOperator Theory: Advances and Applications,$x2296-4878 ;$v229 606 $aPotential theory (Mathematics) 606 $aHarmonic analysis 606 $aOperator theory 606 $aPotential Theory 606 $aAbstract Harmonic Analysis 606 $aOperator Theory 615 0$aPotential theory (Mathematics). 615 0$aHarmonic analysis. 615 0$aOperator theory. 615 14$aPotential Theory. 615 24$aAbstract Harmonic Analysis. 615 24$aOperator Theory. 676 $a515.2433 701 $aAlmeida$b Alexandre$01755691 701 $aCastro$b Luis$01755692 701 $aSpeck$b F.-O$g(Frank-Olme)$0441776 701 $aSamko$b S. G$g(Stefan Grigorevich)$028230 712 12$aIDOTA 2011 (Meeting)$f(2011 :$eAveiro, Portugal) 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910437865603321 996 $aAdvances in harmonic analysis and operator theory$94192602 997 $aUNINA