Operator Theory, Pseudo-Differential Equations, and Mathematical Physics

1. Front Matter

   Pages i-xxv

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2. The Dirichlet Problem for the Heat Equation in Domains with Cuspidal Points on the Boundary

   • Alexandra Antoniouk, Nikolai Tarkhanov

   Pages 1-20

3. Globally Bisingular Elliptic Operators

   • U. Battisti, T. Gramchev, L. Rodino, S. Pilipović

   Pages 21-38

4. The Index Formula of Douglas for Block Toeplitz Operators on the Bergman Space of the Ball

   • Albrecht Böttcher, Antti Perälä

   Pages 39-55

5. The Green Function and Optical Field Enhancement in a Multilayered Microsphere with Metamaterial

   • Gennadiy Burlak, Vladimir Rabinovich

   Pages 57-72

6. Potential Methods for Anisotropic Pseudo-Maxwell Equations in Screen Type Problems

   • O. Chkadua, R. Duduchava, D. Kapanadze

   Pages 73-93

7. Functions of Noncommuting Operators in an Asymptotic Problem for a 2D Wave Equation with Variable Velocity and Localized Right-hand Side

   • Sergey Dobrokhotov, Dmitrii Minenkov, Vladimir Nazaikinskii, Brunello Tirozzi

   Pages 95-125

8. On Toeplitz and Hankel Operators with Oscillatory Symbols Containing Blaschke Products and Applications to the KdV Equation

   • Sergei Grudsky, Alexei Rybkin

   Pages 127-150

9. Mellin Quantisation in Corner Operators

   • N. Habal, B.-W. Schulze

   Pages 151-172

10. Pseudodifferential Operators on Variable Lebesgue Spaces

    • Alexei Yu. Karlovich, Ilya M. Spitkovsky

    Pages 173-183

11. On Convolution Type Operators with Piecewise Slowly Oscillating Data

    • Yuri I. Karlovich, Iván Loreto Hernández

    Pages 185-207

12. Transmutations and Spectral Parameter Power Series in Eigenvalue Problems

    • Vladislav V. Kravchenko, Sergii M. Torba

    Pages 209-238

13. Estimate from Below for the Growth of Solution to the Navier-Stokes Equation When the Solution Blows Up

    • Valeri V. Kucherenko

    Pages 239-259

14. Some New Scales of Weight Characterizations of Hardy-type Inequalities

    • Alois Kufner, Lars-Erik Persson, Natasha Samko

    Pages 261-274

15. Almost Periodic Elliptic Equations: Sub- and Super-solutions

    • Gaston M. N’Guérékata, Alexander Pankov

    Pages 275-292

16. Morrey-Campanato Spaces: an Overview

    • Humberto Rafeiro, Natasha Samko, Stefan Samko

    Pages 293-323

17. Arveson Dichotomy and Essential Fractality

    • Steffen Roch

    Pages 325-342

18. Lower Bounds for the Counting Function of Integral Operators

    • Y. Safarov

    Pages 343-354

19. Toeplitz Operators on the Bergman Spaces with Pseudodifferential Defining Symbols

    • Armando Sánchez-Nungaray, Nikolai Vasilevski

    Pages 355-374

20. Finite Sections of Band-dominated Operators – Norms, Condition Numbers and Pseudospectra

    • Markus Seidel, Bernd Silbermann

    Pages 375-390

This volume is a collection of papers devoted to the 70th birthday of Professor Vladimir Rabinovich. The opening article (by Stefan Samko) includes a short biography of Vladimir Rabinovich, along with some personal recollections and bibliography of his work. It is followed by twenty research and survey papers in various branches of analysis (pseudodifferential operators and partial differential equations, Toeplitz, Hankel, and convolution type operators, variable Lebesgue spaces, etc.) close to Professor Rabinovich's research interests. Many of them are written by participants of the International workshop “Analysis, Operator Theory, and Mathematical Physics” (Ixtapa, Mexico, January 23–27, 2012) having a long history of scientific collaboration with Vladimir Rabinovich, and are partially based on the talks presented there.The volume will be of great interest to researchers and graduate students in differential equations, operator theory, functional and harmonic analysis, and mathematical physics.​

• Toeplitz and convolution type operators
• operator algebras
• problems of mathematical physics
• pseudo-differential equations
• symbol calculus
• partial differential equations

• de Morelos, Facultad de Ciencias, Universidad Autónoma del Estado, Cuernavaca, Mexico

  Yuri I. Karlovich

• , Dipartimento di Matematica, Università di Torino, Torino, Italy

  Luigi Rodino

• , Fakultät für Mathematik, Technische Universität Chemnitz, Chemnitz, Germany

  Bernd Silbermann

• , Department of Mathematics, College of William and Mary, Williamsburg, USA

  Ilya M. Spitkovsky

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