相关论文: Some topics in complex and harmonic analysis, 5

These informal notes deal with Fourier series in one or more variables, Fourier transforms in one variable, and related matters.

These notes, associated with a topics course, deal with some special cases involving norms and linear transformations.

We prove an inverse relation and a family of convolution formulas involving partial Bell polynomials. Known and some presumably new combinatorial identities of convolution type are discussed. Our approach relies on an interesting…

In the second part of the paper we consider a convolution of probability measures on spaces of locally finite configurations (subsets of a phase space) as well as their connection with the convolution of the corresponding correlation…

This note is concerned in so called harmonic complex structures introduced by the author previously. I will recall some previous results and emphasize the motivation: Provide an attempt to a fundamental problem in geometry--determining the…

By applying the derivative operators to Chu-Vandermonde convolution, several general harmonic number identities are established.

We introduce the notion of filtration between topologies and study its stabilization properties. Descriptive set theoretic complexity plays a role in this study. Filtrations lead to natural transfinite sequences approximating a given…

In this paper, we study some properties of associated sequences of special polynomials. From the properties of associated sequences of polynomials, we derive some interesting identities of special polynomials.

We introduce the associated Lah numbers. Some recurrence relations and convolution identities are established. An extension of the associated Stirling and Lah numbers to the r-Stirling and r-Lah numbers are also given. For all these…

These notes briefly discuss basic notions concerning locally compact abelian topological groups and Fourier transforms of functions on them.

In these notes we briefly consider various situations related to infinite commutative semigroups, connected to convolutions and Fourier transforms.

We consider two types of convolutions ($\ast$ and $\star$) of functions on spaces of finite configurations (finite subsets of a phase space), and some their properties are studied. A connection of the $\ast$-convolution with the convolution…

We present various identities in the form of convolutions involving Stirling numbers of both kinds, Lah numbers, and binomial coefficients. Certain convolution polynomials are discussed also. The proofs are based on several series…

This paper surveys some selected topics in the theory of conformal metrics and their connections to complex analysis, partial differential equations and conformal differential geometry.

This note deals with certain properties of convex functions. We provide results on the convexity of the set of minima of these functions, the behaviour of their subgradient set under restriction, and optimization of these functions over an…

In this paper we give refinements of some convex and log-convex moment inequalities of the first and second order using a special kind of positive semi-definite form. An open problem concerning eight parameter refinement of second order is…

On the basis of the generalizations of the Jacobi identity found by the author some identities satisfied by the curvature and torsion of a covariant differentiation are derived. A kind of the generalized covariant differentiation is…

The relation between representations and positive definite functions is a key concept in harmonic analysis on topological groups. Recently this relation has been studied on topological groupoids. This is the second in a series of papers in…

This is Part II of the series of our papers under the title "Toward resolution of singularities over a field of positive characteristic (The Idealistic Filtration Program)". See http://arxiv.org/abs/math/0607009 for Part I.

We briefly review the basic ideas behind archetypal analysis for matrix factorization and discuss its behavior in approximating the convex hull of a data sample. We then ask how good such approximations can be and consider different cases.…