Related papers: A theorem concerning Fourier transforms: A survey
In this contribution we generalize the classical Fourier Mellin transform [S. Dorrode and F. Ghorbel, Robust and efficient Fourier-Mellin transform approximations for gray-level image reconstruction and complete invariant description,…
We study the properties of different type of transforms by means of operational methods and discuss the relevant interplay with many families of special functions. We consider in particular the binomial transform and its generalizations. A…
In this PhD thesis we discuss, develop and apply this fascinating theory connected to modern harmonic analysis. In particular we make new estimations of Vilenkin-Fourier coefficients and prove some new results concerning boundedness of…
Hardy's type uncertainty principle on connected nilpotent Lie groups for the Fourier transform is proved. An analogue of Hardy's theorem for Gabor transform has been established for connected and simply connected nilpotent Lie groups.…
This article presents a convenient approach to Fourier analysis for the investigation of functions and distributions defined in $\mathbb{T}^m \times \mathbb{R}^n$. Our approach involves the utilization of a mixed Fourier transform,…
I discuss the present situation with regard to a variety of theoretical topics in hadronic spin physics: (a) global analysis of the g1 data---positivity at leading and next-to-leading order, renormalisation-scheme dependence,…
We prove theorems of interest about the recently given $\Lambda^{r}$-strong convergence. We extend the results of F. M\'oricz [On $\Lambda$-strong convergence of numerical sequences and Fourier series, Acta Math.~Hungar., 54 (1989),…
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.…
In this paper we develop a theory of Fourier-like transforms on the space of stable graphs. In particular, we introduce a duality theory of stable graphs. As an application, we derive the holomorphic anomaly equations for general…
The transference theory for Lp spaces of Calderon, Coifman, and Weiss is a powerful tool with many applications to singular integrals, ergodic theory, and spectral theory of operators. Transference methods afford a unified approach to many…
This paper deals with continuous and compact mappings of the Fourier transform in function spaces with dominating mixed smoothness.
The Hilbert transform is a multiplier operator and is widely used in the theory of Fourier transforms. The Hilbert transform was the motivation for the development of modern harmonic analysis. Its discrete version is also widely used in…
How to study a nice function on the real line? The physically motivated Fourier theory technique of harmonic analysis is to expand the function in the basis of exponentials and study the meaningful terms in the expansion. Now, suppose the…
We give a generalization of Beurling's theorem for the Clifford-Fourier transform. Then, analogues of Hardy, Cowling-Price and Gelfand-Shilov theorems are obtained in Clifford analysis.
These notes briefly discuss basic notions concerning locally compact abelian topological groups and Fourier transforms of functions on them.
This book deals with the theory of generalized algebraic transformations, which is elaborated with the aim to provide a relatively simple theoretical tool that enables an exact treatment of diverse more complex lattice-statistical models.…
This comprehensive review paper delves into the intricacies of advanced Fourier type integral transforms and their mathematical properties, with a particular focus on fractional Fourier transform (FrFT), linear canonical transform (LCT),…
Applications of harmonic analysis on finite groups were recently introduced to measure partition problems, with a variety of equipartition types by convex fundamental domains obtained as the vanishing of prescribed Fourier transforms.…
This manuscript presents shortly the results obtained by participants of the scientific seminar which is held more than twenty years under leadership of the author at Donetsk University. In the list of references main publications are…
For each $f\!:\!\mathbb{R}\to\mathbb{C}$ that is Henstock--Kurzweil integrable on the real line, or is a distribution in the completion of the space of Henstock--Kurzweil integrable functions in the Alexiewicz norm, it is shown that the…