Related papers: Harmonic Analysis Techniques in Several Complex Va…
This paper develops a theory of analytic geometry over the field with one element. The approach used is the analytic counter-part of the Toen-Vaquie theory of schemes over F_1, i.e. the base category relative to which we work out our theory…
The subject of this PhD thesis is harmonic analysis on solvable extensions of H-type groups. Let N be an H-type group and S=NA be its solvable extension of rank one. The author study the weak type 1 boundedness of suitable Hardy-Littlewood…
The intention of this survey to collect in one paper many recent results and advances related with Bergman type projection acting in various spaces of analytic functions in several complex variables in the unit ball, tubular domains over…
The main aim of this paper is to construct explicitly orthogonal bases for the spaces of k-homogeneous polynomial solutions of the Hodge-de Rham system in the Euclidean space R^m which take values in the space of s-vectors. Actually, we…
The predictions of mean-field electrodynamics can now be probed using direct numerical simulations of random flows and magnetic fields. When modelling astrophysical MHD, it is important to verify that such simulations are in agreement with…
We discuss $QCD$ in the Hamiltonian frame work. We treat finite density $QCD$ in the strong coupling regime. We present a parton-model inspired regularisation scheme to treat the spectrum ($\theta$-angles) and distribution functions in…
This is a brief summary of our studies of quantum field theories in a special limit in which the instantons are present, the anti-instantons are absent, and the perturbative corrections are reduced to one-loop. We analyze the corresponding…
We apply modern techniques of dyadic harmonic analysis to obtain sharp estimates for the Bergman projection in weighted Bergman spaces. Our main theorem focuses on the Bergman projection on the Hartogs triangle. The estimates of the…
Despite the advances in the development of numerical methods analytical approaches still play the key role on the way towards a deeper understanding of many-particle systems. In this regards, diagonalization schemes for Hamiltonians…
The Hardy spaces are defined on the quotient domain of a bounded complete Reinhardt domain by a finite subgroup of $U(n)$. The Szeg\H{o} projection on the quotient domain can be studied by lifting to the covering space. This setting builds…
In this short survey article, we showcase a number of non-trivial geometric problems that have recently been resolved by marrying methods from functional calculus and real-variable harmonic analysis. We give a brief description of these…
We prove various representations and density results for Hardy spaces of holomorphic functions for two classes of bounded domains in $\mathbb C^n$, whose boundaries satisfy minimal regularity conditions (namely the classes $C^2$ and…
We study the existence of uniformly bounded extension and trace operators for W^{1,p}-functions on randomly perforated domains, where the geometry is assumed to be stationary ergodic. Such extension and trace operators are important for…
Homology has long been accepted as an important computable tool for quantifying complex structures. In many applications, these structures arise as nodal domains of real-valued functions and are therefore amenable only to a numerical study…
In this paper, we show a new relation between phase transition in one-dimensional Statistical Mechanics and the multiplicity of the dimension of the space of harmonic functions for an extension of the classical transfer operator. We…
A spectral sequence calculating the homology groups of some spaces of maps equivariant under compact group actions is described. For the main example, we calculate the rational homology groups of spaces of even and odd maps $S^m \to S^M$,…
We use methods of harmonic analysis and group representation theory to study the spectral properties of the abstract parabolic operator $\mathscr L = -d/dt+A$ in homogeneous function spaces. We provide sufficient conditions for…
The following two inversion methods for Radon-like transforms are widely used in integral geometry and related harmonic analysis. The first method invokes mean value operators in accordance with the classical Funk-Radon-Helgason scheme. The…
The main contributions of this paper are the proposition and the convergence analysis of a class of inertial projection-type algorithm for solving variational inequality problems in real Hilbert spaces where the underline operator is…
We establish a new perturbation theory for orthogonal polynomials using a Riemann--Hilbert approach and consider applications in numerical linear algebra and random matrix theory. This new approach shows that the orthogonal polynomials with…