Related papers: Moutard transform for the generalized analytic fun…
This application of nonstandard analysis utilizes the notion of the highly-staturated enlargement. These nonstandard methods clarify many aspects of the theory of generalized functions (distributions).
In this paper, certain generalized fractional derivative formulae are introduced involving the k-Mittag-Leffler function. Then their image formulae (using Beta transform, Laplace transform and Whittaker transform) are also established. The…
A transduction provides us with a way of using the monadic second-order language of a structure to make statements about a derived structure. Any transduction induces a relation on the set of these structures. This article presents a…
Gel'fand triples of test and generalized functionals in Gaussian spaces are constructed and characterized.
We consider one-parameter families of quadratic-phase integral transforms which generalize the fractional Fourier transform. Under suitable regularity assumptions, we characterize the one-parameter groups formed by such transforms.…
We study basic properties of the generalized ideal transforms $D_I(M, N)$ and the set of associated primes of the modules $R^iD_I(M,N).$
A general divergence measure for monotonic functions is introduced. Its connections with the f-divergence for convex functions are explored. The main properties are pointed out.
Tnis paper deals with some special integral transforms in the setting of quaternionic valued slice polyanalytic functions. In particular, using the polyanalytic Fueter mappings it is possible to construct a new family of polynomials which…
In this article we introduce a generalization of the Newton transformation to the case of a system of endomorphisms. We show that it can be used in the context of extrinsic geometry of foliations and distributions yielding new integral…
Using the recently defined concept of Taylor measures, we propose a generalization of Taylor's theorem to measurable, non-analytic functions, that do not require differentiation. We study consequences of the generalization, including the…
We describe an abstract 2-categorical setting to study various notions of polynomial and analytic functors and monads.
This investigation pertains to the construction of a class of generalised deformed derivative operators which furnish the familiar finite difference and the q-derivatives as special cases. The procedure involves the introduction of a linear…
We discuss the notion of the orbifold transform, and illustrate it on simple examples. The basic properties of the transform are presented, including transitivity and the exponential formula for symmetric products. The connection with the…
Discrete analogs of the index transforms with squares of Bessel functions of the first and second kind $J_\nu(z),\ Y_\nu(z)$ are introduced and investigated. The corresponding inversion theorems for suitable classes of functions and…
We introduce an amalgam type space, a subspace of $L^1(\mathbb R_+).$ Integrability results for the Fourier transform of a function with the derivative from such an amalgam space are proved. As an application we obtain estimates for the…
We work with semi-algebraic functions on arbitrary real closed fields. We generalize the notion of critical values and prove a Sard type theorem in our framework.
Extending the work of Freese, we further develop the theory of generalized trigonometric functions. In particular, we study to what extent the notion of polar form for the complex numbers may be generalized to arbitrary associative…
The concept of generalized functions taking values in a differentiable manifold is extended to a functorial theory. We establish several characterization results which allow a global intrinsic formulation both of the theory of…
Based on Colombeau's theory of algebras of generalized functions we introduce the concepts of generalized functions taking values in differentiable manifolds as well as of generalized vector bundle homomorphisms. We study their basic…
In this paper we discuss generalized group, provides some interesting examples. Further we introduce a generalized module as a module like structure obtained from a generalized group and discuss some of its properties and we also describes…