相关论文: Potpourri, 5
The note complements topological aspects of the theory of chiral algebras.
We study the combinatorics of the contributions to the form factor of the group U(N) in the large $N$ limit. This relates to questions about semiclassical contributions to the form factor of quantum systems described by the unitary…
The goal of this work is to introduce and study fuzzy limits of functions. Two approaches to fuzzy limits of a function are considered. One is based on the concept of a fuzzy limit of a sequence, while another generalizes the conventional…
This is an introduction to The Theme Issue on "Free Boundary Problems and Related Topics", which consists of 14 survey/review articles on the topics, of Philosophical Transactions of the Royal Society A: Physical, Mathematical and…
This is a survey on eigenfunctions of the Laplacian on Riemannian manifolds (mainly compact and without boundary). We discuss both local results obtained by analyzing eigenfunctions on small balls, and global results obtained by wave…
New cases of the multiplicity conjecture are considered.
This article discusses several matters related to Sobolev, Poincare, and isoperimetric inequalities in various settings.
This thesis consists of Chapters 1 and 2. The main results are contained in the two preprints and two published papers, listed below. Chapter 1 deals with conformal invariants in the euclidean space Rn; n >= 2; and their interrelation. In…
These notes give an elementary approach to parts of the theory of standard Borel and analytic spaces.
We study boundary properties of plurisubharmonic functions near real submanifolds of almost complex manifolds.
The problem of replacing an integral norm with respect to a given probability measure by the corresponding integral norm with respect to a discrete measure is discussed in the paper. The above problem is studied for elements of finite…
We formulate some problems and conjectures about semigroups of rational functions under composition. The considered problems arise in different contexts, but most of them are united by a certain relationship to the concept of amenability.
This paper deals with Poisson processes on an arbitrary measurable space. Using a direct approach, we derive formulae for moments and cumulants of a vector of multiple Wiener-It\^o integrals with respect to the compensated Poisson process.…
We define a notion which contains numerous basic notions of Analysis as special cases, for example limit, continuity, differential, Riemann and Lebesgue integral, root and exponential functions. Properties like additivity or linearity of…
We survey recent work on normal functions, including limits and singularities of admissible normal functions, the Griffiths-Green approach to the Hodge conjecture, algebraicity of the zero-locus of a normal function, Neron models, and…
Consider an eigenfunction of the Laplacian on a torus. How small can its $L^2$-norm be on small balls? We provide partial answers to this question by exploiting the distribution of integer points on spheres, basic properties of polynomials,…
The potential applications of boundary functionals of random processes, such as the extreme values of these processes, the moment of first reaching a fixed level, the value of the process at the moment of reaching the level, the moment of…
We study a metric-like structure on categories, showing that the concept of the limit of a sequence in a metric space and the concept of the colimit of a sequence in a category have a common generalization. The main concept is a norm on a…
We consider approximately greater than relations on fuzzy sets and discuss their properties.
These notes contain everything necessary to run a flipped course on "The Atmosphere" at an introductory undergraduate level. There are notes for the students to read before each course meeting and problems for them to work on in small…