Related papers: Vector partition function and generalized Dahmen-M…
In this paper we discuss some topics related to the general theory of frames. In particular we focus our attention to the existence of different 'reconstruction formulas' for a given vector of a certain Hilbert space and to some refinement…
The paper is devoted to the index theory of orbital and transverse elliptic operators on manifolds with a proper Lie group action. It corrects errors of my previous paper (published in JNCG in 2016) on transverse operators and contains new…
This paper provides some first steps in developing empirical process theory for functions taking values in a vector space. Our main results provide bounds on the entropy of classes of smooth functions taking values in a Hilbert space, by…
We prove identities generating higher dimensional vector partitions. We derive theorems for integer lattice points in the 2D first quadrant, then generalize the approach to find 3D and $n$-space lattice point vector region extensions. We…
The aim of the present paper is, firstly we study the concepts of (m, (q_1, ..., q_d))- partial isometries on a Hilbert space, secondly, we introduce the notion of m- invertibility of tuples of operators as a natural generalization of the…
Even though matrix model partition functions do not exhaust the entire set of tau-functions relevant for string theory, they seem to be elementary building blocks for many others and they seem to properly capture the fundamental symplicial…
The tools, ideas, and insights from linear algebra, abstract algebra, and functional analysis can be extremely useful to signal processing and system theory in various areas of engineering, science, and social science including…
We present some general theorems about operator algebras that are algebras of functions on sets, including theories of local algebras, residually finite dimensional operator algebras and algebras that can be represented as the scalar…
This habilitation thesis centres on linearisation of vector-valued functions which means that vector-valued functions are represented by continuous linear operators. The first question we face is which vector-valued functions may be…
This paper gives an exposition of well known results on vector partition functions. The exposition is based on works of M. Brion, A. Szenes and M. Vergne and is geared toward explicit computer realizations. In particular, the paper presents…
We suggest a generalization of vector calculus for the case of non-integer dimensional space. The first and second orders operations such as gradient, divergence, the scalar and vector Laplace operators for non-integer dimensional space are…
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…
We compute the partition and correlation generating functions for the Heisenberg intertwiner generalized vertex operator algebra on a genus $g$ Riemann surface in the Schottky uniformization. These are expressed in terms of differential…
New index transforms are investigated, which contain as the kernel products of the Bessel and modified Bessel functions. Mapping properties and invertibility in Lebesgue spaces are studied for these operators. Relationships with the…
In the first part we show that a vector-valued almost separably valued function $f$ is holomorphic (harmonic) if and only if it is dominated by an $L^1_\mathrm{loc}$ function and there exists a separating set $W\subset X'$ such that…
We use Gelfand-Tsetlin diagrams to write down the weight multiplicity function for the Lie algebra sl_k(C) (type A_{k-1}) as a single partition function. This allows us to apply known results about partition functions to derive interesting…
We first strictly expressed the basic notions and research methods of abstract operators, which systematically expounded the main results of abstract operator theory. By combining abstract operators with the Laplace transform, we can easily…
We present two new proofs of the exchange theorem for the Laplace transformation of vector-valued distributions. We then derive an explicit solution to the Dirichlet problem of the polyharmonic operator in a half-space. Finally, we obtain…
New index transforms, involving squares of Kelvin functions, are investigated. Mapping properties and inversion formulas are established for these transforms in Lebesgue spaces. The results are applied to solve a boundary value problem on…
We explore functors between operator space categories, some properties of these functors, and establish relations between objects in these categories and their images under these functors, in particular regarding injectivity and injective…