Related papers: Complex-Order Scale-Invariant Operators and Self-S…
In this article, we impose a new class of fractional analytic functions in the open unit disk. By considering this class, we define a fractional operator, which is generalized Salagean and Ruscheweyh differential operators. Moreover, by…
We study differential operators associated with families of polynomials orthonormal with respect to certain measures. These operators, when applied to the Fourier transforms of such measures, produce basis functions for expansions of…
We consider fractional differentiation operators in various senses and show that the strictly accretive property is the common property of fractional differentiation operators. Also we prove that the sectorial property holds for…
Symmetry is present in many tasks in computer vision, where the same class of objects can appear transformed, e.g. rotated due to different camera orientations, or scaled due to perspective. The knowledge of such symmetries in data coupled…
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…
On conformal manifolds of even dimension $n\geq 4$ we construct a family of new conformally invariant differential complexes. Each bundle in each of these complexes appears either in the de Rham complex or in its dual. Each of the new…
The real theory of the Dunkl operators has been developed very extensively, while there still lacks the corresponding complex theory. In this paper we introduce the complex Dunkl operators for certain Coxeter groups. These complex Dunkl…
We develop the concept of operators in Hilbert spaces which are similar to their adjoints via antiunitary operators, the latter being not necessarily involutive. We discuss extension theory, refined polar and singular-value decompositions,…
We propose a fast and stable method for constructing matrix approximations to fractional integral operators applied to series in the Chebyshev fractional polynomials. This method utilizes a recurrence relation satisfied by the fractional…
We study fractional differential equations of Riemann-Liouville and Caputo type in Hilbert spaces. Using exponentially weighted spaces of functions defined on $\mathbb{R}$, we define fractional operators by means of a functional calculus…
We construct new, efficient, and accurate high-order finite differencing operators which satisfy summation by parts. Since these operators are not uniquely defined, we consider several optimization criteria: minimizing the bandwidth, the…
Generalizing the algebra of motion-invariant differential operators on a symmetric space we study invariant operators on equivariant vector bundles. We show that the eigenequation is equivalent to the corresponding eigenequation with…
In this paper we will take under consideration subordinators and their inverse processes (hitting-times). We will present in general the governing equations of such processes by means of convolution-type integro-differential operators…
We consider Fourier integral operators with symbols in modulation spaces and non-smooth phase functions whose second orders of derivatives belong to certain types of modulation space. We establish continuity and Schatten-von Neumann…
Signal scaling is a fundamental operation of practical importance in which a signal is enlarged or shrunk in the coordinate direction(s). Scaling or magnification is not trivial for signals of a discrete variable since the signal values may…
A formal fourth order differential operator with a singular coefficient that is a linear combination of the Dirac delta-function and its derivatives is considered. The asymptotic behavior of spectra and eigenfunctions of a family of…
A chain rule for power product is studied with fractional differential operators in the framework of Sobolev spaces. The fractional differential operators are defined by the Fourier multipliers. The chain rule is considered newly in the…
In [1], an operator was introduced which acts parallel to the Riemann-Liouville differintegral on a transformation of the space of real analytic functions and commutes with itself. This paper aims to extend the technique - and its defining…
In their work on differential operators in positive characteristic, Smith and Van den Bergh define and study the derived functors of differential operators; they arise naturally as obstructions to differential operators reducing to positive…
We give a formula for the derivatives of a correlation function of composite operators with respect to the parameters (i.e., the strong fine structure constant and the quark mass) of QCD in four-dimensional euclidean space. The formula is…