LEADER 07974nam 2200589 450 001 9910508462503321 005 20230510093636.0 010 $a3-030-75425-1 035 $a(MiAaPQ)EBC6803486 035 $a(Au-PeEL)EBL6803486 035 $a(CKB)19410490600041 035 $a(OCoLC)1286430115 035 $a(PPN)258838973 035 $a(EXLCZ)9919410490600041 100 $a20220815d2021 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 00$aFrom operator theory to orthogonal polynomials, combinatorics, and number theory $ea volume in honor of Lance Littlejohn's 70th birthday /$fFritz Gesztesy, Andrei Martinez-Finkelshtein, editors 210 1$aCham, Switzerland :$cBirkha?user,$d[2021] 210 4$d©2021 215 $a1 online resource (388 pages) 225 1 $aOperator theory, advances and applications ;$vVolume 285 311 08$aPrint version: Gesztesy, Fritz From Operator Theory to Orthogonal Polynomials, Combinatorics, and Number Theory Cham : Springer International Publishing AG,c2022 9783030754242 320 $aIncludes bibliographical references. 327 $aIntro -- Preface -- References -- Contents -- Compositions and Chebyshev Polynomials -- 1 Introduction -- 2 Proof of Theorem 1 -- 3 Proof of Theorem 2 -- 4 Proof of Theorem 3 -- 5 Proofs of Theorems 4 and Corollary 1 -- 6 Proof of Theorem 6 and Corollaries -- 7 Further Topics -- References -- Non-negative Extensions of Hamiltonian Systems -- 1 Introduction -- 2 Preliminaries -- 3 The Friedrichs Extension TF of T0 -- 4 Characterisation of Non-negative Extensions TB -- 5 Example: A Fourth Order ODE -- References -- On Simon's Hausdorff Dimension Conjecture -- 1 Introduction -- 2 A Weak Version of Simon's Hausdorff Dimension Conjecture -- 2.1 A Basic Estimate -- 2.2 Prüfer Variables -- 2.3 Unboundedness and Infinite Energy -- 2.4 Proof of Theorem 1.1 and Corollary 1.2 -- References -- Hypergeometric Functions over Finite Fields and Modular Forms: A Survey and New Conjectures -- 1 Introduction -- 2 Preliminaries -- 3 Weight Two Newforms -- 4 Higher Weight Newforms -- 4.1 The Conjectures of Rodriguez Villegas -- 4.2 Conjectures of Evans -- 4.3 Relations with Ramanujan's ?-Function -- 4.4 Other Relations -- 5 Trace Formulas for Hecke Operators -- 6 New Relations -- References -- Ballistic Transport for Periodic Jacobi Operators on Zd -- 1 Introduction -- 2 Decomposition of J -- 3 Ballistic Motion -- References -- Perspectives on General Left-Definite Theory -- 1 Introduction -- 1.1 Notation -- 2 Sturm-Liouville Operators -- 3 Left-Definite Theory -- 4 Comparison with BKV Semi-Bounded Form Theory -- 5 Scale of Spaces from Singular Perturbation Theory -- 6 Perturbation Setup -- Appendix: Extension Theory -- References -- Sampling in the Range of the Analysis Operator of a Continuous Frame Having Unitary Structure -- 1 Statement of the Problem -- 2 Some Preliminaries -- 2.1 Continuous and Discrete Frames. 327 $a2.2 Discrete Convolution Systems and Frames of Translates -- 3 The Subspace of L2(G) Where the Sampling Is Carried Out -- 3.1 Sampling Data as a Filtering Process -- 4 The Main Sampling Result and Consequences -- 4.1 Sampling at a Subgroup R with Finite Index in H -- 4.2 Additional Notes and Remarks -- 4.3 The Case of a Semi-Direct Product of Groups -- Euclidean Motion Group and Crystallographic Subgroups -- 4.4 Some Final Comments -- References -- An Extension of the Coherent Pair of Measures of the Second Kind on the Unit Circle -- 1 Introduction -- 2 Coherent Pairs of Measures of the Second Kind -- 2.1 The Case d?1(z) = 12?i zdz -- 2.2 The Case d?1(z)=1|z-u|212?i zdz, u?0 -- 2.3 A General Case -- 3 Hessenberg Matrices -- 4 Sobolev OPUC -- References -- Bessel-Type Operators and a Refinement of Hardy's Inequality -- 1 Introduction -- 2 An Exactly Solvable, Strongly Singular, Periodic Schrödinger Operator -- 3 A Refinement of Hardy's Inequality -- A.1 The Weyl-Titchmarsh-Kodaira m-Function Associated with Ts,F -- B.1 Remarks on Hardy-Type Inequalities -- References -- Spectral Theory of Exceptional Hermite Polynomials -- 1 Introduction -- 2 Some Spectral Theory -- 3 The Formal Theory of Exceptional Hermite Polynomials -- 3.1 Multi-Step Factorization Chains -- 3.2 The Norm Identity -- 4 The L2 Theory -- References -- Occupation Time for Classical and Quantum Walks -- 1 Introduction -- 2 A Look at the Classical Discrete Case -- 3 Occupation Times for Quantum Walks -- 4 A Look at the Hadamard Walk -- 5 The Walk with a Constant Coin -- 6 The Even Verblunsky Coefficients Tend to One -- 7 A Look at the Riesz Walk -- References -- On Foci of Ellipses Inscribed in Cyclic Polygons -- 1 Introduction -- 2 Background and Notation -- 3 The Quadrilateral Case -- 4 The Hexagon Case -- 5 The Pentagon Case -- References -- A Differential Analogue of Favard's Theorem. 327 $a1 Introduction -- 2 The Main Theory -- 2.1 Fundamental Results -- 2.2 Relation to Existing Work -- 3 Examples -- 3.1 Jacobi -- 3.2 Hermite -- 3.3 Generalized Hermite -- 3.4 Laguerre -- 3.5 Generalized Laguerre -- 3.6 Continuous Hahn -- 4 Computational Considerations -- 4.1 Computation of Expansion Coefficients -- 4.2 Approximation Theory on the Real Line -- 5 Periodic Bases Arising from Discrete Orthogonal Polynomials -- 6 Challenges and Outlook -- 6.1 Transform Pairs -- 6.2 Location of Zeros -- 6.3 Sobolev Orthogonality -- 6.4 Beyond the Canonical Form -- 6.5 A Freudian Slip-Why We Need More Polynomials -- References -- Intrinsic Properties of Strongly Continuous Fractional Semigroups in Normed Vector Spaces -- 1 Introduction -- 2 Background -- 2.1 Logarithmic Norms on Banach Spaces -- 2.2 Logarithmic Norm Bounds of Classical Semigroups -- 3 Fractional Semigroups -- 3.1 Mittag-Leffler and Wright Functions -- 3.2 Logarithmic Norm Bounds of Fractional Semigroups -- 4 Conclusions and Future Endeavors -- References -- The BFK-gluing Formula for Zeta-determinants and the Conformal Rescaling of a Metric -- 1 Introduction -- 2 The Metric Rescaling and Invariance Theory -- 3 Proof of Theorem 1 -- 4 Conclusions -- References -- New Representations of the Laguerre-Sobolev and Jacobi-Sobolev Orthogonal Polynomials -- 1 Introduction -- 2 Two Representations of the Laguerre-Sobolev Polynomials -- 3 New Representations of the Jacobi-Sobolev Polynomials -- References -- Compactness, or Lack Thereof, for the Harmonic Double Layer -- 1 Compactness of the Harmonic Double Layer Operator on Lebesgue Spaces -- 2 Failure of Compactness for the Harmonic Double Layer Operator -- References -- Weighted Chebyshev Polynomials on Compact Subsets of the Complex Plane -- 1 Introduction -- 2 Existence, Uniqueness, and Characterization of Weighted Chebyshev Polynomials. 327 $a3 Bounds for Weighted Chebyshev Polynomials -- References -- The Eichler Integral of E2 and q-brackets of t-hook Functions -- 1 Introduction and Statement of Results -- 2 Nuts and Bolts -- 2.1 A Formula of Han -- 2.2 A Formula of Berndt -- 3 Proofs of Results -- 4 Some Examples -- References. 410 0$aOperator theory, advances and applications ;$vVolume 285. 606 $aOperator theory 606 $aSpectral theory (Mathematics) 606 $aTeoria espectral (Matemàtica)$2thub 606 $aTeoria d'operadors$2thub 608 $aHomenatges$2thub 608 $aLlibres electrònics$2thub 615 0$aOperator theory. 615 0$aSpectral theory (Mathematics) 615 7$aTeoria espectral (Matemàtica) 615 7$aTeoria d'operadors 676 $a515.724 702 $aGesztesy$b Fritz$f1953- 702 $aMarti?nez Finkelshtein$b Andrei 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910508462503321 996 $aFrom operator theory to orthogonal polynomials, combinatorics, and number theory$92904759 997 $aUNINA