Related papers: J\"org Eschmeier's mathematical work
In this paper we give an attempt to extend some arithmetic properties such as multiplicativity, convolution products to the setting of operators theory. We provide a significant examples which are of interest in number theory. We also give…
In this exposition, I discuss several developments in the theory of vertex operator algebras, and I include motivation for the definition.
The article surveys the main techniques and results of the spectral theory of periodic operators arising in mathematical physics and other areas. Close attention is paid to studying analytic properties of Bloch and Fermi varieties, which…
We provide an introduction to mathematical theory of scattering resonances and survey some recent results.
This is a pedagogic introduction to certain aspects of inverse spectral theory for Schr\"{o}dinger operators and Jacobi matrices that revolves around my joint work with Fritz Gesztesy whose $70^{th}$ birthday we are honoring.
This paper is concerned with a certain aspect of the spectral theory of unitary operators in a Hilbert space and its aim is to give an explicit construction of continuous functions of unitary operators. Starting from a given unitary…
To appear in Encyclopedia of Mathematical Physics, J.-P. Fran\c{c}oise, G. Naber and T.S. Tsou, eds., Elsevier, 2006. The article surveys the modern developments of noncommutative geometry in string theory.
To appear in Encyclopedia of Mathematical Physics, published by Elsevier in early 2006. Comments/corrections welcome. The article surveys topological aspects in gauge theories.
The paper contains a survey of the results obtained during the last ten years in the theory of elliptic boundary problems in H\"ormander function spaces, developed by the authors, and other related results of modern analysis. The basics of…
This is a survey of accumulated spectral analysis observations spanning more than a century, referring to the double layer potential integral equation, also known as Neumann-Poincar\'e operator. The very notion of spectral analysis has…
The main objective of this paper is to develop a notion of joint spectrum for complex solvable Lie algebras of operators acting on a Banach space, which generalizes the Taylor joint spectrum (T.J.S.) for several commuting operators.
In this paper we investigate the spectral and the scattering theory of Schr\"odinger operators acting on perturbed periodic discrete graphs. The perturbations considered are of two types: either a multiplication operator by a short-range or…
These notes offer a unified introduction to spectral methods for the study of complex systems. They are intended as an operative manual rather than a theorem-proof textbook: the emphasis is on tools, identities, and perspectives that can be…
Estimates for eigenvalues of Schr\"{o}dinger operators on the half-line with complex-valued potentials are established. Schr\"{o}dinger operators with potentials belonging to weak Lebesque's classes are also considered. The results cover…
In this paper we investigate the spectral and scattering theory for operators acting on topological crystals and on their perturbations. A special attention is paid to perturbations obtained by the addition of an infinite number of edges,…
The aim of this text is to provide a linguistically accessible, but comprehensive introduction into a variety of topics in dynamical systems and its applications. Whilst preliminary knowledge of dynamical systems is useful, it is not…
We provide an introduction to the old-standing problem of isometric immersions. We combine a historical account of its multifaceted advances, which have fascinated geometers and analysts alike, with some of the applications in the…
This survey presents an overview of the advances around Tverberg's theorem, focusing on the last two decades. We discuss the topological, linear-algebraic, and combinatorial aspects of Tverberg's theorem and its applications. The survey…
We give a brief overview of the life and combinatorics of Jeff Remmel, a mathematician with successful careers in both logic and combinatorics.
We give an overview of several works of Victor Katsnelson published in 1965--1970, and pertaining to the complex and harmonic analysis and the spectral theory.