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We introduce a unified framework for the construction of convolutions and product formulas associated with a general class of regular and singular Sturm-Liouville boundary value problems. Our approach is based on the application of the…
In this paper, further to the point interaction method for inverse Sturm-Liouville problems on finite intervals firstly proposed in our previous work, we will continue to generalize this method to the inverse eigenvalue problems for…
In this paper, a Sturm-Liouville boundary value problem equiped with conformable fractional derivates is considered. We give some uniqueness theorems for the solutions of inverse problems according to the Weyl function, two given spectra…
Several new properties of weighted Hilbert transform are obtained. If mu is zero, two Plancherel-like equations and the isotropic properties are derived. For mu is real number, a coerciveness is derived and two iterative sequences are…
Given three transversal and sufficiently regular hypersurfaces in R^3 it follows from work of Bennett-Carbery-Wright that the convolution of two L^2 functions supported of the first and second hypersurface, respectively, can be restricted…
This is the first part of a series of papers where the behaviour of the invariants under twist by Dirichlet characters is studied for $L$-functions of degree 2. Here we show, under suitable conditions, that degree and internal shift remain…
Bernstein polynomials, long a staple of approximation theory and computational geometry, have also increasingly become of interest in finite element methods. Many fundamental problems in interpolation and approximation give rise to…
Most of the known Fourier transforms associated with the equations of mathematical physics have a trivial kernel, and an inversion formula as well as the Parseval equality are fulfilled. In other words, the system of the eigenfunctions…
We introduce here a method which uses etale neighborhoods to extend results from smooth semi-local rings to arbitrary semi-local rings A by passing to the henselization of a smooth presentation of A. The technique is used to show that etale…
A new coupling argument is introduced to establish Driver's integration by parts formula and shift Harnack inequality. Unlike known coupling methods where two marginal processes with different starting points are constructed to move…
The classical Beurling-Helson-Lowdenslager theorem characterizes the shift-invariant subspaces of the Hardy space $H^{2}$ and of the Lebesgue space $L^{2}$. In this paper, which is self-contained, we define a very general class of norms…
We consider Sturm-Liouville operators on geometrical graphs without cycles (trees) with singular potentials from the class $W_2^{-1}$. We suppose that the potentials are known on a part of the graph, and study the so-called partial inverse…
In this paper we adapt the method of [P. H. Baptistelli, M. Manoel and I. O. Zeli. Normal form theory for reversible equivariant vector fields. Bull. Braz. Math. Soc., New Series 47 (2016), no. 3, 935-954] to obtain normal forms of a class…
We prove a new family of inequalities, which compare the integral of a geometric convolution of non-negative functions with the integrals of the original functions. For classical inf-convolution, this type of inequality is called the…
New high statistics data from the second generation of ultrarelativistic heavy-ion experiments open up new possibilities in terms of data analysis. To fully utilize the potential we propose to analyze the $m_\perp$-spectra of hadrons using…
The general evolution kernels of the twist 2 light-ray operators for unpolarized and polarized deep inelastic scattering are calculated in ${\cal O}(\alpha_s)$. From these evolution kernels a series of special evolution equations can be…
Stieltjes integral theorem is more commonly known by the phrase 'integration by parts' and enables rearrangement of an otherwise intractable integral to a more amenable form; often permitting completion of an integral in closed form.…
This paper is devoted to the study of a convolution structure denoted by $*_{\alpha}$, which is defined via the Hartley--Bessel transform. This concept was introduced in a recent work by F. Bouzeffour [\emph{J. Pseudo-Differ. Oper. Appl.},…
A simple proof is provided to show that any bounded normal operator on a real Hilbert space is orthogonally equivalent to its transpose(adjoint). A structure theorem for invertible skew-symmetric operators, which is analogous to the finite…
Dans cette note, nous donnons une autre d\'emonstration du r\'esultat d\'emontr\'e par D. Barlet dans http://aif.cedram.org/aif-bin/fitem?id=AIF_2010__60_1_319_0 (arXiv:0809.4981), en nous appuyant sur la transformation de Mellin et des…