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This volume is dedicated to the memory of Sergey Naboko
(1950-2020). In addition to original research contributions
covering the vast areas of interest of Sergey Naboko, it includes
personal reminiscences and comments on the works and legacy of
Sergey Naboko’s scientific achievements. Areas from complex
analysis to operator theory, especially, spectral theory, are
covered, and the papers will inspire current and future researchers
in these areas.
The main topics of this volume, dedicated to Lance Littlejohn, are
operator and spectral theory, orthogonal polynomials,
combinatorics, number theory, and the various interplays of these
subjects. Although the event, originally scheduled as the Baylor
Analysis Fest, had to be postponed due to the pandemic, scholars
from around the globe have contributed research in a broad range of
mathematical fields. The collection will be of interest to both
graduate students and professional mathematicians. Contributors
are: G.E. Andrews, B.M. Brown, D. Damanik, M.L. Dawsey, W.D. Evans,
J. Fillman, D. Frymark, A.G. Garcia, L.G. Garza, F. Gesztesy, D.
Gomez-Ullate, Y. Grandati, F.A. Grunbaum, S. Guo, M. Hunziker, A.
Iserles, T.F. Jones, K. Kirsten, Y. Lee, C. Liaw, F. Marcellan, C.
Markett, A. Martinez-Finkelshtein, D. McCarthy, R. Milson, D.
Mitrea, I. Mitrea, M. Mitrea, G. Novello, D. Ong, K. Ono, J.L.
Padgett, M.M.M. Pang, T. Poe, A. Sri Ranga, K. Schiefermayr, Q.
Sheng, B. Simanek, J. Stanfill, L. Velazquez, M. Webb, J.
Wilkening, I.G. Wood, M. Zinchenko.
This is the second part of a two volume anthology comprising a
selection of 49 articles that illustrate the depth, breadth and
scope of Nigel Kalton's research. Each article is accompanied by
comments from an expert on the respective topic, which serves to
situate the article in its proper context, to successfully link
past, present and hopefully future developments of the theory and
to help readers grasp the extent of Kalton's accomplishments.
Kalton's work represents a bridge to the mathematics of tomorrow,
and this book will help readers to cross it. Nigel Kalton
(1946-2010) was an extraordinary mathematician who made major
contributions to an amazingly diverse range of fields over the
course of his career.
This book is the first part of a two volume anthology comprising a
selection of 49 articles that illustrate the depth, breadth and
scope of Nigel Kalton's research. Each article is accompanied by
comments from an expert on the respective topic, which serves to
situate the article in its proper context, to successfully link
past, present and hopefully future developments of the theory, and
to help readers grasp the extent of Kalton's accomplishments.
Kalton's work represents a bridge to the mathematics of tomorrow,
and this book will help readers to cross it. Nigel Kalton
(1946-2010) was an extraordinary mathematician who made major
contributions to an amazingly diverse range of fields over the
course of his career.
This is the second part of a two volume anthology comprising a
selection of 49 articles that illustrate the depth, breadth and
scope of Nigel Kalton's research. Each article is accompanied by
comments from an expert on the respective topic, which serves to
situate the article in its proper context, to successfully link
past, present and hopefully future developments of the theory and
to help readers grasp the extent of Kalton's accomplishments.
Kalton's work represents a bridge to the mathematics of tomorrow,
and this book will help readers to cross it. Nigel Kalton
(1946-2010) was an extraordinary mathematician who made major
contributions to an amazingly diverse range of fields over the
course of his career.
These lecture notes aim at providing a purely analytical and
accessible proof of the Callias index formula. In various branches
of mathematics (particularly, linear and nonlinear partial
differential operators, singular integral operators, etc.) and
theoretical physics (e.g., nonrelativistic and relativistic quantum
mechanics, condensed matter physics, and quantum field theory),
there is much interest in computing Fredholm indices of certain
linear partial differential operators. In the late 1970's,
Constantine Callias found a formula for the Fredholm index of a
particular first-order differential operator (intimately connected
to a supersymmetric Dirac-type operator) additively perturbed by a
potential, shedding additional light on the Fedosov-Hoermander
Index Theorem. As a byproduct of our proof we also offer a glimpse
at special non-Fredholm situations employing a generalized Witten
index.
This book is the first part of a two volume anthology comprising a
selection of 49 articles that illustrate the depth, breadth and
scope of Nigel Kalton's research. Each article is accompanied by
comments from an expert on the respective topic, which serves to
situate the article in its proper context, to successfully link
past, present and hopefully future developments of the theory, and
to help readers grasp the extent of Kalton's accomplishments.
Kalton's work represents a bridge to the mathematics of tomorrow,
and this book will help readers to cross it. Nigel Kalton
(1946-2010) was an extraordinary mathematician who made major
contributions to an amazingly diverse range of fields over the
course of his career.
The main topics of this volume, dedicated to Lance Littlejohn, are
operator and spectral theory, orthogonal polynomials,
combinatorics, number theory, and the various interplays of these
subjects. Although the event, originally scheduled as the Baylor
Analysis Fest, had to be postponed due to the pandemic, scholars
from around the globe have contributed research in a broad range of
mathematical fields. The collection will be of interest to both
graduate students and professional mathematicians. Contributors
are: G.E. Andrews, B.M. Brown, D. Damanik, M.L. Dawsey, W.D. Evans,
J. Fillman, D. Frymark, A.G. Garcia, L.G. Garza, F. Gesztesy, D.
Gomez-Ullate, Y. Grandati, F.A. Grunbaum, S. Guo, M. Hunziker, A.
Iserles, T.F. Jones, K. Kirsten, Y. Lee, C. Liaw, F. Marcellan, C.
Markett, A. Martinez-Finkelshtein, D. McCarthy, R. Milson, D.
Mitrea, I. Mitrea, M. Mitrea, G. Novello, D. Ong, K. Ono, J.L.
Padgett, M.M.M. Pang, T. Poe, A. Sri Ranga, K. Schiefermayr, Q.
Sheng, B. Simanek, J. Stanfill, L. Velazquez, M. Webb, J.
Wilkening, I.G. Wood, M. Zinchenko.
As a partner to Volume 1: Dimensional Continuous Models, this
monograph provides a self-contained introduction to
algebro-geometric solutions of completely integrable, nonlinear,
partial differential-difference equations, also known as soliton
equations. The systems studied in this volume include the Toda
lattice hierarchy, the Kac-van Moerbeke hierarchy, and the
Ablowitz-Ladik hierarchy. An extensive treatment of the class of
algebro-geometric solutions in the stationary as well as
time-dependent contexts is provided. The theory presented includes
trace formulas, algebro-geometric initial value problems,
Baker-Akhiezer functions, and theta function representations of all
relevant quantities involved. The book uses basic techniques from
the theory of difference equations and spectral analysis, some
elements of algebraic geometry and especially, the theory of
compact Riemann surfaces. The presentation is constructive and
rigorous, with ample background material provided in various
appendices. Detailed notes for each chapter, together with an
exhaustive bibliography, enhance understanding of the main results.
This book is about algebro-geometric solutions of completely integrable nonlinear partial differential equations in (1+1)-dimensions; also known as soliton equations. Explicitly treated integrable models include the KdV, AKNS, sine-Gordon, and Camassa-Holm hierarchies as well as the classical massive Thirring system. An extensive treatment of the class of algebro-geometric solutions in the stationary and time-dependent contexts is provided. The formalism presented includes trace formulas, Dubrovin-type initial value problems, Baker-Akhiezer functions, and theta function representations of all relevant quantities involved. The book uses techniques from the theory of differential equations, spectral analysis, and elements of algebraic geometry (most notably, the theory of compact Riemann surfaces).
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