Related papers: Functional Analysis
We are used to thinking of an operator acting once, twice, and so on. However, an operator acting integer times can be consistently analytic continued to an operator acting complex times. Applications: (s,r) diagrams and an extension of…
This article was prepared in connection with the 2009 Barnett lecture at the University of Cincinnati, and deals with various classes of fractal sets and analysis on them.
These notes present a first graduate course in harmonic analysis. The first part emphasizes Fourier series, since so many aspects of harmonic analysis arise already in that classical context. The Hilbert transform is treated on the circle,…
Brief Description: The book provides a unique highly self-contained text introducing the reader to the classical and modern theory of polyanalytic functions and their generalizations. This is a subbranch of complex analysis of several…
Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to…
A tutorial review is given of some developments and applications of stochastic processes from the point of view of the practicioner physicist. The index is the following: 1.- Introduction 2.- Stochastic Processes 3.- Transient Stochastic…
The subject of this textbook is the analysis of Boolean functions. Roughly speaking, this refers to studying Boolean functions $f : \{0,1\}^n \to \{0,1\}$ via their Fourier expansion and other analytic means. Boolean functions are perhaps…
This survey is based on a series of lectures given during the \emph{School on Random Schr\"odinger Operators} and the \emph{International Conference on Spectral Theory and Mathematical Physics} at the Pontificia Universidad Catolica de…
Various notions of dissipativity type for partial differential operators and their applications are surveyed. We deal with functional dissipativity and its particular case $L^p$-dissipativity. Most of the results are due to the authors.
This text is meant for analysis students who want to learn more about the effects of the axiom of choice on functional analysis, and the things that may go wrong in its absence. As this is a text aimed for analysis students, we will not…
These are lecture notes for the course "Analysis and X-ray tomography". The course is a broad overview of various tools in analysis that can be used to study X-ray tomography. The focus is on tools and ideas, not so much on technical…
The functional interpretation is a systematic, syntactic method for transforming certain non-constructive proofs into constructive proofs with explicit bounds. We illustrate the interpretation by working through a concrete, fairly simple…
This is a brief survey of recent results by the authors devoted to one of the most important operators of integral geometry. Basic facts about the analytic family of cosine transforms on the unit sphere and the corresponding Funk transform…
In the first part of these short lecture notes, we will present an introduction on (auto-)correlation functions and linear-response functions in the language of a physicist. In particular, the fluctuation-dissipation theorem in classical…
We study some number theory problems related to the harmonic analysis (Fourier bases) of the Cantor set introduced by Jorgensen and Pedersen in \cite{JP98}.
Perhaps, it is not too far from the truth to say that, among the great concepts (as compactness, completeness, order, convexity) on which functional analysis is based, connectedness is relatively less popular, though this does not mean that…
Fourier Transforms is a first in a series of monographs we present on harmonic analysis. Harmonic analysis is one of the most fascinating areas of research in mathematics. Its centrality in the development of many areas of mathematics such…
We review recent progress in operator algebraic approach to conformal quantum field theory. Our emphasis is on use of representation theory in classification theory. This is based on a series of joint works with R. Longo.
Motivated by modern observational studies, we introduce a class of functional models that expands nested and crossed designs. These models account for the natural inheritance of correlation structure from sampling design in studies where…
These lectures introduce the basic ideas and practices of statistical analysis for particle physicists, using a real-world example to illustrate how the abstractions on which statistics is based are translated into practical application.