06073nam 22008295 450 991043786560332120251230060936.09783034805162303480516010.1007/978-3-0348-0516-2(CKB)2670000000342861(EBL)1156185(OCoLC)831115879(SSID)ssj0000878409(PQKBManifestationID)11469122(PQKBTitleCode)TC0000878409(PQKBWorkID)10836040(PQKB)10109824(DE-He213)978-3-0348-0516-2(MiAaPQ)EBC1156185(PPN)168307383(MiFhGG)9783034805162(EXLCZ)99267000000034286120130130d2013 u| 0engur|n|---|||||txtccrAdvances in Harmonic Analysis and Operator Theory The Stefan Samko Anniversary Volume /edited by Alexandre Almeida, Luís Castro, Frank-Olme Speck1st ed. 2013.Basel :Springer Basel :Imprint: Birkhäuser,2013.1 online resource (387 p.)Operator Theory: Advances and Applications,2296-4878 ;229Description based upon print version of record.9783034807937 3034807937 9783034805155 3034805152 Advances 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, 1970-19775. 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: 1993-20036.4. 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 Iα() (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 Operators1. 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 functions2.5. 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; ReferencesEnergy Flow Above the Threshold of Tunnel EffectThis 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.Operator Theory: Advances and Applications,2296-4878 ;229Potential theory (Mathematics)Harmonic analysisOperator theoryPotential TheoryAbstract Harmonic AnalysisOperator TheoryPotential theory (Mathematics).Harmonic analysis.Operator theory.Potential Theory.Abstract Harmonic Analysis.Operator Theory.515.2433Almeida Alexandre1755691Castro Luis1755692Speck F.-O(Frank-Olme)441776Samko S. G(Stefan Grigorevich)28230IDOTA 2011 (Meeting)(2011 :Aveiro, Portugal)MiAaPQMiAaPQMiAaPQBOOK9910437865603321Advances in harmonic analysis and operator theory4192602UNINA