Modern Methods in Operator Theory and Harmonic Analysis: OTHA 2018, Rostov-on-Don, Russia, April 22-27, Selected, Revised and Extended Contributions

Preface......Page 6
Professor Garnik Karapetyan (1958/02/03–2018/11/29)......Page 8
Professor Stasys Rutkauskas (1951/06/06–2018/10/29)......Page 11
Contents......Page 13
Part I Function Theory and Approximation Theory......Page 16
 1 Introduction......Page 17
 2 Some General Properties of Operators in Local Morrey-Type Spaces......Page 19
 3 Transition to Global Morrey-Type Spaces for Operators, Commuting with a Shift Operator......Page 34
 4 The Criterion of the Embedding of a Weighted Lorentz Space into a Morrey-Type Space. Notation and Main Results......Page 36
 5 Proofs of Results Formulated in Sect.4......Page 39
 References......Page 47
 1 Introduction......Page 49
 2 Young Functions and Orlicz Spaces......Page 51
 3 Parabolic Fractional Maximal Function in Orlicz Spaces......Page 53
 4 Parabolic Fractional Maximal Commutators in Orlicz Spaces......Page 56
 References......Page 62
 1 Introduction......Page 64
 2 Proof of Theorem 1.8......Page 66
 References......Page 69
 1 Introduction......Page 70
 2 Preliminaries......Page 71
 3 Hölder Type Spaces of Holomorphic Functions in the Unit Disc......Page 73
 4 Boundedness of Holomorphic Projection in Generalized Hölder Spaces of Holomorphic Functions in mathbbD......Page 75
 5 Generalized Hölder Type Spaces of Harmonic Functions in the Unit Disc and Boundedness of Harmonic Projection......Page 77
 References......Page 78
 1 Introduction......Page 80
 2 Multiplicative Completion of Some Subsystems  of the Double Trigonometric System......Page 82
  2.1 The Case Ωc={(0,0)}......Page 83
  2.2 The Case Ωc = 0timesZZ......Page 85
  2.3 The Case Ωc = 0timesZZ0......Page 89
 References......Page 91
 1 Introduction......Page 93
 2 Main Results......Page 95
 3 Adjoint Operators......Page 98
 4 Reformulations for mathcalH......Page 100
 5 More General Hausdorff Operators......Page 101
 References......Page 103
 1 Introduction......Page 104
 2 Clifford Algebras......Page 106
 3 Hypercomplex Structures of mathbbRn+1......Page 107
 4 Calculus of Alternative Hypercomplex Differential Forms......Page 109
 5 Hypercomplex Derivability......Page 112
 6 Hypercomplex Differentiability......Page 113
 7 Generalized Power Series......Page 114
  8.1 Definition and Some Properties......Page 118
  8.2 A Matrix Approach......Page 120
  8.3 Orthogonality......Page 122
 References......Page 124
 1 Introduction......Page 127
  2.1 Schwartz Distributions and the Fourier Transform......Page 130
  2.3 Estimates in Besov–Morrey Spaces......Page 133
  3.1 Paraproduct......Page 135
  3.2 Resonant Part......Page 136
  3.3 Conclusion of the Proof of Theorem1......Page 138
 4 Commutator Estimate......Page 139
 References......Page 142
Part II Functional Analysis and Operator Theory......Page 144
Analogs of the Khintchin—Kolmogorov Inequalities in Discrete Morrey Spaces......Page 145
 1 Introduction and Preliminaries......Page 146
 2 Main Results......Page 149
 3 Proofs of Theorems2–4......Page 154
 References......Page 159
 1 Mellin Convolution Equations—Are They Useful?......Page 160
 2 Mellin Convolution Equations: Definition and Fredholm Properties......Page 162
 3 Banach Algebra of Operators Generated by Mellin  and Fourier Convolutions......Page 167
 4 Mellin Convolution Equations in the Bessel Potential Spaces......Page 173
 References......Page 180
 1 Problem Setup......Page 182
 2 Properties of the Operators Upm, U......Page 186
 3 The mathcalL-Convolution Operator......Page 189
 4 The mathcalL-Wiener-Hopf Operator......Page 193
 References......Page 204
  1.1 Statement of the Problem......Page 205
  1.2 Setting, Goals and Tools......Page 206
  1.3 Overview and Related Topics......Page 207
  2.1 Main Syzygy......Page 208
  2.2 Thin Spectrum......Page 209
  3.1 Multiple Roots......Page 211
  3.2 Desingularization Through Deformation......Page 212
  3.3 A-Equivalence and Topological Equivalence......Page 213
  4.2 Patterns......Page 215
  4.3 Generalized Euler-Jacobi Formula......Page 216
  4.4 Example......Page 217
  5.1 Triple Points: Two-Step Algorithm......Page 218
  5.2 Spectrum at Non-isolated Fixed Points......Page 220
 References......Page 221
 1 Introduction......Page 223
 2 Preliminaries......Page 225
 3 Factorization of Lattice Multimorphisms......Page 228
 4 Factorization of Order Bounded Disjointness Preserving Operators......Page 231
 5 Factorization of Symmetric Lattice Multimorphisms......Page 235
 6 The Associate f-Algebra Multimorphism......Page 238
 References......Page 241
 1 Problem Description......Page 243
 2 Markov Decision Processes and Q-Learning......Page 245
 3 Robbins–Monro Conditions for Persistent Exploration Learning Strategies......Page 248
 References......Page 253
 1 Introduction......Page 254
 2 Results......Page 256
 3 Proofs......Page 259
 References......Page 265
The Distance Function and Boundedness of Diameters of the Nearest Elements......Page 267
 References......Page 276
Part III Differential Equations and Mathematical Physics......Page 277
 1 Introduction......Page 278
 2 Assumptions......Page 282
 3 Representation of Solutions......Page 284
  3.1 Considerations in the Hyperbolic Zone......Page 288
  3.2 Considerations in the Oscillation Subzone......Page 292
  3.3 Considerations in the Elliptic Zone......Page 293
  3.4 Considerations in the Dissipative Zone......Page 299
  3.5 Considerations in the Reduced Zone......Page 303
 4 Gluing Procedure......Page 305
  4.1 Preliminaries......Page 309
  4.2 Final Estimates......Page 310
 5 Energy Estimates for Solutions to Damped Wave Models with Additional Regularity of the Data......Page 311
 6 Some Examples......Page 313
 References......Page 318
 1 Introduction. Formulation of the Results......Page 320
  1.1 Historical Remarks......Page 321
  1.2 Formulation of the Results......Page 322
  2.1 Some Preliminary Results......Page 325
  2.2 The Case, When the Multiplicity of the i Is Grater  Than Two......Page 328
  2.3 The Case, When the Multiplicity of the i Is Equal Two......Page 332
 References......Page 337
 1 Introduction......Page 339
 2 Preliminaries......Page 341
  3.1 A General Result for rinIR......Page 347
  3.2 Uniqueness and Globality......Page 351
  3.3 Conservation of Energy and Well-Posedness......Page 352
  3.4 Regularity......Page 353
  3.5 A Special Case of Solutions......Page 356
 4 Solutions in Unbounded Sets......Page 358
 References......Page 363
 1 Introduction......Page 365
 2 Setting Up the Problem......Page 366
 3 Sufficient Condition for Completeness of General Systems of Solutions and for Continuity of the Systems  at Infinity......Page 367
 4 Necessary and Sufficient Condition for Completeness of the General Systems of Solutions......Page 370
 References......Page 372
 1 Introduction......Page 373
 2 A Transmutation Operator and a Representation  for the Solution......Page 374
 3 A Fourier-Legendre Series Representation  for the Kernels γj......Page 378
 4 The Neumann Series of Bessel Functions Representation of the Solution......Page 379
  5.1 The SPPS Representation......Page 382
  5.2 Numerical Illustrations......Page 383
 6 Application to Order n>4......Page 386
 References......Page 387
 1 Introduction. Formulation of the Problem......Page 388
 2 Some Auxiliary Results......Page 389
 3 Main Theorems......Page 393
 References......Page 398
A Numerical Realization of the Wiener–Hopf Method for the Kolmogorov Backward Equation......Page 399
 1 Introduction......Page 400
 2 Problem Setup......Page 402
 3 Heston Model Case......Page 404
  4.1 Substitution......Page 406
  4.2 Carr\'s Randomization......Page 407
  4.3 Markov Chain Approximation and Recurrent Calculations......Page 410
  5.1 General Formulae......Page 413
  5.2 Approximate and Explicit Factorization......Page 415
  5.3 Fast Fourier Transform Implementation......Page 416
 6 Numerical Experiments......Page 418
 7 Conclusion......Page 423
 References......Page 424
 1 Introduction......Page 427
 3 Free Vibrations......Page 429
 4 Dispersion Equation Structure......Page 430
 5 Properties of Equation Solution......Page 432
 6 Asymptotic Analysis......Page 433
 7 Problem Statements......Page 434
 8 Properties of Problems 1AS, 1A, 1Aβ and 1B......Page 437
 9 The Numerical Solution Scheme......Page 443
 10 Forced Oscillations. Residue Calculation......Page 444
 11 Numerical Test......Page 447
 References......Page 448
 1 Differential Systems on the Half-Line......Page 450
 2 Differential Systems on a Finite Interval......Page 455
 3 Differential Systems on the Half-Line with Multiplied Roots of the Characteristic Polynomial......Page 465
 4 Differential Systems on a Finite Interval with Multiplied Roots of the Characteristic Polynomial......Page 470
 References......Page 473