Related papers: On the regularity of generic Hausdorff-type transf…
Combining the derivative operator with Chu-Vandermonde convolution, we establish a class of summation formulas on generalized harmonic numbers.
We give an explicit formula for the Hankel transform of a regular sequence in terms of the coefficients of the associated orthogonal polynomials and the sequence itself. We apply this formula to some sequences of combinatorial interest,…
We consider nonlocal equations of order larger than one with measure data and prove gradient regularity in Sobolev and H\"older spaces as well as pointwise bounds of the gradient in terms of Riesz potentials, leading to fine regularity…
In the context of kernel optimization, we prove a result that yields new factorizations and realizations. Our initial context is that of general positive operator-valued kernels. We further present implications for Hilbert space-valued…
An abstract mathematical framework is presented in this paper as a unification of several deformed or generalized algebra proposed recently in the context of generalized statistical theories intended to treat certain complex thermodynamic…
We show continuity in generalized weighted Morrey spaces of sub-linear integral operators generated by some classical integral operators and commutators. The obtained estimates are used to study global regularity of the solution of the…
In the relativistic and the nonrelativistic theoretical treatment of moderate and high-power laser-matter interaction, the generalized Bessel function occurs naturally when a Schr\"odinger-Volkov and Dirac-Volkov solution is expanded into…
The basic concepts of classical mechanics are given in the operator form. The dynamical equation for a hybrid system, consisting of quantum and classical subsystems, is introduced and analyzed in the case of an ideal nonselective…
Starting with the Heisenberg-Weyl algebra, fundamental to quantum physics, we first show how the ordering of the non-commuting operators intrinsic to that algebra gives rise to generalizations of the classical Stirling Numbers of…
In this paper, we establish a condition on the coefficients of differential operators generated in the space of square-integrable functions on the entire real line by an ordinary differential expression with periodic, complex-valued…
Following to the Weil method we generalize the Heisenberg-Robertson uncertainty relation for arbitrary two operators. Consideration is made in spherical coordinates, where the distant variable is restricted from one side, . By this reason…
We prove a nonlinear regularity principle in sequence spaces which produces universal estimates for special series defined therein. Some consequences are obtained and, in particular, we establish new inclusion theorems for multiple summing…
We obtain Calder\'on-Zygmund type estimates in generalized Morrey spaces for nonlinear equations of $p$-Laplacian type. Our result is obtained under minimal regularity assumptions both on the operator and on the domain. This result allows…
The one-sided and full Hilbert transforms are evaluated exactly by means of the method of finite-part integration [E.A. Galapon, \textit{Proc. Roy. Soc. A} \textbf{473}, 20160567 (2017)]. In general, the result consists of two terms -- the…
This note contributes to a circle of ideas that we have been developing recently in which we view certain abstract operator algebras $H^{\infty}(E)$, which we call Hardy algebras, and which are noncommutative generalizations of classical…
We present an approach to generalized Riordan arrays which is based on operations in one large group of lower triangular matrices. This allows for direct proofs of many properties of weighted Sheffer sequences, and shows that all the groups…
We introduce new techniques allowing one to construct diagonals of bounded Hilbert space operators and operator tuples under "Blaschke-type" assumptions. This provides a new framework for a number of results in the literature and…
We prove a generalization of van der Corput's difference theorem for sequences of vectors in a Hilbert space. This generalization is obtained by establishing a connection between sequences of vectors in the first Hilbert space with a vector…
We study the behaviour of linear partial differential operators with polynomial coefficients via a Wigner type transform. In particular, we obtain some results of regularity in the Schwartz space $\mathcal S$ and in the space ${\mathcal…
This survey paper reports on the properties of the fourth-order Bessel-type linear ordinary differential equation, on the generated self-adjoint differential operators in two associated Hilbert function spaces, and on the generalisation of…