Ebook: Operator Theory, Pseudo-Differential Equations, and Mathematical Physics: The Vladimir Rabinovich Anniversary Volume

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.​

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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 and the bibliography of Vladimir Rabinovich’s works, along with personal recollections. 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), who have a long history of scientific collaboration with Rabinovich and whose contributions are partially based on the talks presented at that meeting. The volume will be of great interest to researchers and graduate students working in the fields of differential equations, operator theory, functional and harmonic analysis and mathematical physics.

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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 and the bibliography of Vladimir Rabinovich’s works, along with personal recollections. 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), who have a long history of scientific collaboration with Rabinovich and whose contributions are partially based on the talks presented at that meeting. The volume will be of great interest to researchers and graduate students working in the fields of differential equations, operator theory, functional and harmonic analysis and mathematical physics.
Content:
Front Matter....Pages i-xxv
The Dirichlet Problem for the Heat Equation in Domains with Cuspidal Points on the Boundary....Pages 1-20
Globally Bisingular Elliptic Operators....Pages 21-38
The Index Formula of Douglas for Block Toeplitz Operators on the Bergman Space of the Ball....Pages 39-55
The Green Function and Optical Field Enhancement in a Multilayered Microsphere with Metamaterial....Pages 57-72
Potential Methods for Anisotropic Pseudo-Maxwell Equations in Screen Type Problems....Pages 73-93
Functions of Noncommuting Operators in an Asymptotic Problem for a 2D Wave Equation with Variable Velocity and Localized Right-hand Side....Pages 95-125
On Toeplitz and Hankel Operators with Oscillatory Symbols Containing Blaschke Products and Applications to the KdV Equation....Pages 127-150
Mellin Quantisation in Corner Operators....Pages 151-172
Pseudodifferential Operators on Variable Lebesgue Spaces....Pages 173-183
On Convolution Type Operators with Piecewise Slowly Oscillating Data....Pages 185-207
Transmutations and Spectral Parameter Power Series in Eigenvalue Problems....Pages 209-238
Estimate from Below for the Growth of Solution to the Navier-Stokes Equation When the Solution Blows Up....Pages 239-259
Some New Scales of Weight Characterizations of Hardy-type Inequalities....Pages 261-274
Almost Periodic Elliptic Equations: Sub- and Super-solutions....Pages 275-292
Morrey-Campanato Spaces: an Overview....Pages 293-323
Arveson Dichotomy and Essential Fractality....Pages 325-342
Lower Bounds for the Counting Function of Integral Operators....Pages 343-354
Toeplitz Operators on the Bergman Spaces with Pseudodifferential Defining Symbols....Pages 355-374
Finite Sections of Band-dominated Operators – Norms, Condition Numbers and Pseudospectra....Pages 375-390
On the Reduction of Linear Systems Related to Boundary Value Problems....Pages 391-406

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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 and the bibliography of Vladimir Rabinovich’s works, along with personal recollections. 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), who have a long history of scientific collaboration with Rabinovich and whose contributions are partially based on the talks presented at that meeting. The volume will be of great interest to researchers and graduate students working in the fields of differential equations, operator theory, functional and harmonic analysis and mathematical physics.
Content:
Front Matter....Pages i-xxv
The Dirichlet Problem for the Heat Equation in Domains with Cuspidal Points on the Boundary....Pages 1-20
Globally Bisingular Elliptic Operators....Pages 21-38
The Index Formula of Douglas for Block Toeplitz Operators on the Bergman Space of the Ball....Pages 39-55
The Green Function and Optical Field Enhancement in a Multilayered Microsphere with Metamaterial....Pages 57-72
Potential Methods for Anisotropic Pseudo-Maxwell Equations in Screen Type Problems....Pages 73-93
Functions of Noncommuting Operators in an Asymptotic Problem for a 2D Wave Equation with Variable Velocity and Localized Right-hand Side....Pages 95-125
On Toeplitz and Hankel Operators with Oscillatory Symbols Containing Blaschke Products and Applications to the KdV Equation....Pages 127-150
Mellin Quantisation in Corner Operators....Pages 151-172
Pseudodifferential Operators on Variable Lebesgue Spaces....Pages 173-183
On Convolution Type Operators with Piecewise Slowly Oscillating Data....Pages 185-207
Transmutations and Spectral Parameter Power Series in Eigenvalue Problems....Pages 209-238
Estimate from Below for the Growth of Solution to the Navier-Stokes Equation When the Solution Blows Up....Pages 239-259
Some New Scales of Weight Characterizations of Hardy-type Inequalities....Pages 261-274
Almost Periodic Elliptic Equations: Sub- and Super-solutions....Pages 275-292
Morrey-Campanato Spaces: an Overview....Pages 293-323
Arveson Dichotomy and Essential Fractality....Pages 325-342
Lower Bounds for the Counting Function of Integral Operators....Pages 343-354
Toeplitz Operators on the Bergman Spaces with Pseudodifferential Defining Symbols....Pages 355-374
Finite Sections of Band-dominated Operators – Norms, Condition Numbers and Pseudospectra....Pages 375-390
On the Reduction of Linear Systems Related to Boundary Value Problems....Pages 391-406
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