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Differential Equations, Mathematical Physics, and Applications - Selim Grigorievich Krein Centennial (Paperback): Peter... Differential Equations, Mathematical Physics, and Applications - Selim Grigorievich Krein Centennial (Paperback)
Peter Kuchment, Evgeny Semenov
R3,287 R3,099 Discovery Miles 30 990 Save R188 (6%) Ships in 12 - 17 working days

This is the second of two volumes dedicated to the centennial of the distinguished mathematician Selim Grigorievich Krein. The companion volume is Contemporary Mathematics, Volume 733. Krein was a major contributor to functional analysis, operator theory, partial differential equations, fluid dynamics, and other areas, and the author of several influential monographs in these areas. He was a prolific teacher, graduating 83 Ph.D. students. Krein also created and ran, for many years, the annual Voronezh Winter Mathematical Schools, which significantly influenced mathematical life in the former Soviet Union. The articles contained in this volume are written by prominent mathematicians, former students and colleagues of Selim Krein, as well as lecturers and participants of Voronezh Winter Schools. They are devoted to a variety of contemporary problems in ordinary and partial differential equations, fluid dynamics, and various applications.

Harmonic Analysis and Partial Differential Equations - In Honor of Vladimir Maz'ya (Hardcover, 1st ed. 2023): Anatoly... Harmonic Analysis and Partial Differential Equations - In Honor of Vladimir Maz'ya (Hardcover, 1st ed. 2023)
Anatoly Golberg, Peter Kuchment, David Shoikhet
R4,273 Discovery Miles 42 730 Ships in 12 - 17 working days

Over the course of his distinguished career, Vladimir Maz'ya has made a number of groundbreaking contributions to numerous areas of mathematics, including partial differential equations, function theory, and harmonic analysis. The chapters in this volume - compiled on the occasion of his 80th birthday - are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.

Liouville-Riemann-Roch Theorems on Abelian Coverings (Paperback, 1st ed. 2021): Minh Kha, Peter Kuchment Liouville-Riemann-Roch Theorems on Abelian Coverings (Paperback, 1st ed. 2021)
Minh Kha, Peter Kuchment
R1,469 Discovery Miles 14 690 Ships in 10 - 15 working days

This book is devoted to computing the index of elliptic PDEs on non-compact Riemannian manifolds in the presence of local singularities and zeros, as well as polynomial growth at infinity. The classical Riemann-Roch theorem and its generalizations to elliptic equations on bounded domains and compact manifolds, due to Maz'ya, Plameneskii, Nadirashvilli, Gromov and Shubin, account for the contribution to the index due to a divisor of zeros and singularities. On the other hand, the Liouville theorems of Avellaneda, Lin, Li, Moser, Struwe, Kuchment and Pinchover provide the index of periodic elliptic equations on abelian coverings of compact manifolds with polynomial growth at infinity, i.e. in the presence of a "divisor" at infinity. A natural question is whether one can combine the Riemann-Roch and Liouville type results. This monograph shows that this can indeed be done, however the answers are more intricate than one might initially expect. Namely, the interaction between the finite divisor and the point at infinity is non-trivial. The text is targeted towards researchers in PDEs, geometric analysis, and mathematical physics.

Introduction to Quantum Graphs (Hardcover): Gregory Berkolaiko, Peter Kuchment Introduction to Quantum Graphs (Hardcover)
Gregory Berkolaiko, Peter Kuchment
R3,095 Discovery Miles 30 950 Ships in 12 - 17 working days

A ``quantum graph'' is a graph considered as a one-dimensional complex and equipped with a differential operator (``Hamiltonian''). Quantum graphs arise naturally as simplified models in mathematics, physics, chemistry, and engineering when one considers propagation of waves of various nature through a quasi-one-dimensional (e.g., ``meso-'' or ``nano-scale'') system that looks like a thin neighborhood of a graph. Works that currently would be classified as discussing quantum graphs have been appearing since at least the 1930s, and since then, quantum graphs techniques have been applied successfully in various areas of mathematical physics, mathematics in general and its applications. One can mention, for instance, dynamical systems theory, control theory, quantum chaos, Anderson localization, microelectronics, photonic crystals, physical chemistry, nano-sciences, superconductivity theory, etc. Quantum graphs present many non-trivial mathematical challenges, which makes them dear to a mathematician's heart. Work on quantum graphs has brought together tools and intuition coming from graph theory, combinatorics, mathematical physics, PDEs, and spectral theory. This book provides a comprehensive introduction to the topic, collecting the main notions and techniques. It also contains a survey of the current state of the quantum graph research and applications.

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