Related papers: A remark on analytic Fredholm alternative

In this paper, we use a numerical method that involves hybrid and block-pulse functions to approximate solutions of systems of a class of Fredholm and Volterra integro-differential equations. The key point is to derive a new approximation…

In this article, we are considering the Hessian of the area functional in a non-Darboux chart. This does not seem to have been considered before and leads to an interesting new mathematical structure which we introduce in this article and…

For relatively form-compact perturbations of non-negative selfadjoint operators, we obtain an upper bound on the number of discrete eigenvalues in half-planes separated from the positive real axis. The bound is given in terms of a partial…

Let $X$ be a manifold with boundary, and let $L$ be a 0-elliptic operator on X which is semi-Fredholm essentially surjective with infinite-dimensional kernel. Examples include Hodge Laplacians and Dirac operators on conformally compact…

We present a new method to solve in a semianalytical way the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations at NLO order in the x-space. The method allows to construct an evolution operator expressed in form of a rapidly…

In the current article, we establish a distinct version of the operators defined by Berwal \emph{et al.}, which is the Kantorovich type modification of $\alpha$-Bernstein operators to approximate Lebesgue's integrable functions. We define…

The one-dimensional Dunkl operator $D_k$ with a non-negative parameter $k$, is considered under an arbitrary nonlocal boundary value condition. The right inverse operator of $D_k$, satisfying this condition is studied. An operational…

Using some harmonic extensions on the upper-half plane, and probabilistic representations, and curvature-dimension inequalities with some negative dimensions, we obtain some new opimal functional inequalities of the Beckner type for the…

In this work, we develop variational formulations of Petrov-Galerkin type for one-dimensional fractional boundary value problems involving either a Riemann-Liouville or Caputo derivative of order $\alpha\in(3/2, 2)$ in the leading term and…

We provide some new sharp assertions on the action of Toeplitz $T_\varphi$ operator in new $F^{p,q}_\alpha$ type spaces of analytic functions of several complex variables extending previously known assertions proved by various authors.

We prove Brezis--Browder type results for fractional Sobolev spaces and quantitative type estimates for $s$-harmonic functions. Furthermore, we give sufficient conditions for distributional solutions to the fractional Poisson's equation…

In this paper, we continue the study of the polar analytic functions, a notion introduced in \cite{BBMS1} and successfully applied in Mellin analysis. Here we obtain another version of the Cauchy integral formula and a residue theorem for…

In this note known formulas for the product of Toeplitz operators are revisited in the context of their applications to the study of Fredholmness, boundedness of Toeplitz products, and the Berezin-Toeplitz quantization. A few open problems…

We use the theory of abstract Wiener spaces to construct a probabilistic model for Berezin-Toeplitz quantization on a complete Hermitian complex manifold endowed with a positive line bundle. We associate to a function with compact support…

We prove and discuss three results on zero distribution of gaussian analytic functions: (i) the Edeleman-Kostlan formula for the expectation of the counting measure; (ii) a variation on the theme of Calabi's rigidity theorem; (iii) Offord's…

We analytically solve for the time dependent solutions of various density evolution models. With specific forms of the diffusion, drift and sink coefficients, the eigenfunctions can be expressed in terms of hypergeometric functions. We…

We prove spectral properties for random Landau Schr\"odinger operators on $L^2(\mathbb{R}^2)$ with bounded, random potentials supported in a square $\Lambda_L \subset \mathbb{R}^2$ of side length $L>0$, using semiclassical…

Analytic expressions for the Fourier transforms of the Chebyshev and Legendre polynomials are derived, and the latter is used to find a new representation for the half-order Bessel functions. The numerical implementation of the so-called…

This work represents a systematic computational study of the distribution of the Fourier coefficients of cuspidal Hecke eigenforms of level $\Gamma_0(4)$ and half-integral weights. Based on substantial calculations, the question is raised…

Elliptic problems with additional unknown distributions in boundary conditions are investigated in Besov and Sobolev-Triebel-Lizorkin spaces of low regularity, specifically of an arbitrary negative order. We find that the problems induce…