相关论文: Mikusi\'nski's Operational Calculus with Algebraic…
A useful identity relating the infinite sum of two Bessel functions to their infinite integral was discovered in Dominici et al. (2012). Here, we extend this result to products of $N$ Bessel functions, and show it can be straightforwardly…
In this paper we study some boundary operators of a class of Bessel-type Littlewood-Paley extensions whose prototype is \[\Delta_x u(x,y) +\frac{1-2s}{y} \frac{\partial u}{\partial y}(x,y)+\frac{\partial^2 u}{\partial y^2}(x,y)=0 \text{ for…
In a recent paper we unified Bessel functions of different orders .Here we extend the unification to other linairely independant solutions to Bessel equation, Neumann's and Hankel's functions
We solve a version of the Serrin overdetermined problem for the Weinstein operator involving a Bessel operator.
In this paper we consider the generalized little Hankel and Berezin type operators on Besov spaces of holomorphic functions on polydiscs and give results about the boundedness of these operators.
In this work the authors use their contour integral method to derive a double integral connected to the modified Bessel function of the second kind and express it in terms of the Lerch function. There are some useful results relating double…
In this article, we construct operator models for meromorphic functions of bounded type on Krein spaces. This construction is based on certain reproducing kernel Hilbert spaces which are closely related to model spaces. Specifically, we…
Investigation of partial multiplace functions by algebraic methods plays an important role in modern mathematics were we consider various operations on sets of functions, which are naturally defined. The basic operation for $n$-place…
In this paper, we show that the semiclassical calculus recently developed on nilpotent Lie groups and nilmanifolds include the functional calculus of suitable subelliptic operators. Moreover, we obtain Weyl laws for these operators. Amongst…
In this short note we use ideas from systems theory to define a functional calculus for infinitesimal generators of strongly continuous semigroups on a Hilbert space. Among others, we show how this leads to new proofs of (known) results in…
In this article, we define fractal operators motivated by the works of Barnsley and Navascu\'es on various function spaces such as energy space, Lebesgue space, and oscillation space on the well-known fractal domain Sierpi\'nski gasket. We…
Functions like the exponential, Chebyshev polynomials, and monomial symmetric polynomials are preeminent among all special functions. They have simple definitions and can be expressed using easily specified integers like n!. Families of…
A practical solution for the mathematical problem of functional calculus with Laplace-Beltrami operator on surfaces with axial symmetry is found. A quantitative analysis of the spectrum is presented.
We characterize the weights for which we have the boundedness of standard weighted integral operators induced by the Bergman-Besov kernels acting between two general weighted Lebesgue classes on the unit ball of $\mathbb{C}^N$ in terms of…
Motivated by the Poisson equation for the fractional Laplacian on the whole space with radial right hand side, we study global H\"older and Schauder estimates for a fractional Bessel equation. Our methods stand on the so-called semigroup…
In this paper our aim is to present some subordination and superordination results, by using an operator, which involves the normalized form of the generalized Bessel functions of first kind. These results are obtained by investigating some…
We establish new operational formulae of Burchnall type for the complex disk polynomials (generalized Zernike polynomials). We then use them to derive some interesting identities involving these polynomials. In particular, we establish…
A different application of the familiar integral representation for the modifed Bessel function drives to a new Kontorovich-Lebedev-like integral transformation of a general complex index. Mapping and operational properties, a convolution…
Colombeau algebras constitute a convenient framework for performing nonlinear operations like multiplication on Schwartz distributions. Many variants and modifications of these algebras exist for various applications. We present a…
In a recent work, \cite{cgss}, we developed a functional calculus for bounded operators defined on quaternionic Banach spaces. In this paper we show how the results from \cite{cgss} can be extended to the unbounded case, and we highlight…