scholarly journals Paley–Wiener theorem for the q-Bessel transform and associated q-sampling formula

2009 ◽  
Vol 27 (1) ◽  
pp. 55-72 ◽  
Author(s):  
Lazhar Dhaouadi ◽  
Wafa Binous ◽  
Ahmed Fitouhi
Keyword(s):  
Sampling Formula ◽  
Wiener Theorem ◽  
Bessel Transform

scholarly journals Complete transformation of Radon-Kipriyanov. Some properties

2019 ◽  
Vol 489 (2) ◽  
pp. 125-130
Author(s):  
L. N. Lyakhov ◽  
M. G. Lapshina ◽  
S. A. Roshchupkin
Keyword(s):  
Fourier Transform ◽  
Differential Operator ◽  
Differential Operators ◽  
Support Theorem ◽  
Singular Differential Operator ◽  
Wiener Theorem ◽  
Bessel Transform ◽  
Bessel Transforms ◽  
The Fourier Transform ◽  
Complete Transformation

The even Radon-Kipriyanov transform (Kg-transform) is suitable for investigating problems with the Bessel singular differential operator Bi = 2i2+iii,i 0. In this paper, we introduce the odd Radon-Kipriyanov transform and complete Radon-Kipriyanov transform to investigation more general equations containing odd B‑derivativesiBik, k = 0, 1, 2, ... (in particular, gradients of functions). Formulas of K-transforms of singular differential operators are given. Based on the Bessel transforms introduced by B. M. Levitan and the odd Bessel transform introduced by I. A. Kipriyanov and V. V. Katrakhov, a connection was obtained between the complete Radon-Kipriyanov transform with the Fourier transform and the mixed Fourier-Levitan-Kipriyanov-Katrakhov transform. An analogue of Helgasons support theorem and an analogue of the Paley-Wiener theorem are presented.

Titchmarsh's theorem of Hankel transform

2019 ◽  
pp. 11-24
Author(s):  
Mohamed-Ahmed Boudref
Keyword(s):  
Number Theory ◽  
Data Analysis ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Lipschitz Condition ◽  
Analytic Number Theory ◽  
Hankel Transform ◽  
Partial Differential ◽  
Analytic Number ◽  
Bessel Transform

Hankel transform (or Fourier-Bessel transform) is a fundamental tool in many areas of mathematics and engineering, including analysis, partial differential equations, probability, analytic number theory, data analysis, etc. In this article, we prove an analog of Titchmarsh's theorem for the Hankel transform of functions satisfying the Hankel-Lipschitz condition.

A sampling formula for ecological communities with multiple dispersal syndromes

2015 ◽  
Vol 374 ◽  
pp. 94-106 ◽  
Author(s):  
Thijs Janzen ◽  
Bart Haegeman ◽  
Rampal S. Etienne
Keyword(s):  
Ecological Communities ◽  
Sampling Formula ◽  
Dispersal Syndromes

scholarly journals A general sampling formula for community structure data

2017 ◽  
Vol 8 (11) ◽  
pp. 1506-1519 ◽  
Author(s):  
Bart Haegeman ◽  
Rampal S. Etienne
Keyword(s):  
Community Structure ◽  
Structure Data ◽  
Sampling Formula
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