scholarly journals Recovery of compactly supported functions from spectrogram measurements via lifting

2017 ◽  
Author(s):  
Sami Merhi ◽  
Aditya Viswanathan ◽  
Mark Iwen
Keyword(s):  
Compactly Supported ◽  
Compactly Supported Functions

Erdélyi–Kober fractional integrals and radon transforms for mutually orthogonal affine planes

2020 ◽  
Vol 23 (4) ◽  
pp. 967-979
Author(s):  
Boris Rubin ◽  
Yingzhan Wang
Keyword(s):  
Fractional Integrals ◽  
Radon Transforms ◽  
Affine Planes ◽  
Inversion Formulas ◽  
Radial Functions ◽  
Compactly Supported ◽  
Radial Case ◽  
Compactly Supported Functions

AbstractWe apply Erdélyi–Kober fractional integrals to the study of Radon type transforms that take functions on the Grassmannian of j-dimensional affine planes in ℝn to functions on a similar manifold of k-dimensional planes by integration over the set of all j-planes that meet a given k-plane at a right angle. We obtain explicit inversion formulas for these transforms in the class of radial functions under minimal assumptions for all admissible dimensions. The general (not necessarily radial) case, but for j + k = n − 1, n odd, was studied by S. Helgason [8] and F. Gonzalez [4, 5] on smooth compactly supported functions.

scholarly journals Fourier transforms of powers of well-behaved 2D real analytic functions

2018 ◽  
Vol 30 (3) ◽  
pp. 723-732
Author(s):  
Michael Greenblatt
Keyword(s):  
Analytic Functions ◽  
Fourier Transforms ◽  
Newton Polygon ◽  
Companion Paper ◽  
Two Dimensional ◽  
Compactly Supported ◽  
Sharp Estimates ◽  
Real Analytic Functions ◽  
Real Analytic ◽  
Compactly Supported Functions

AbstractThis paper is a companion paper to [6], where sharp estimates are proven for Fourier transforms of compactly supported functions built out of two-dimensional real-analytic functions. The theorems of [6] are stated in a rather general form. In this paper, we expand on the results of [6] and show that there is a class of “well-behaved” functions that contains a number of relevant examples for which such estimates can be explicitly described in terms of the Newton polygon of the function. We will further see that for a subclass of these functions, one can prove noticeably more precise estimates, again in an explicitly describable way.

scholarly journals Higher orbital integrals, Shalika germs, and the Hochschild homology of Hecke algebras

2001 ◽  
Vol 26 (3) ◽  
pp. 129-160 ◽  
Author(s):  
Victor Nistor
Keyword(s):  
Hecke Algebras ◽  
Hochschild Homology ◽  
Cyclic Homology ◽  
Detailed Calculation ◽  
Orbital Integrals ◽  
Compactly Supported ◽  
Shalika Germs ◽  
Definition Of ◽  
Compactly Supported Functions

We give a detailed calculation of the Hochschild and cyclic homology of the algebra𝒞c∞(G)of locally constant, compactly supported functions on a reductivep-adic groupG. We use these calculations to extend to arbitrary elements the definition of the higher orbital integrals introduced by Blanc and Brylinski (1992) for regular semi-simple elements. Then we extend to higher orbital integrals some results of Shalika (1972). We also investigate the effect of the “induction morphism” on Hochschild homology.

scholarly journals Weighted Second-Order Differential Inequality on Set of Compactly Supported Functions and Its Applications

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2830
Author(s):  
Aigerim Kalybay ◽  
Ryskul Oinarov ◽  
Yaudat Sultanaev
Keyword(s):  
Fourth Order ◽  
Differential Inequality ◽  
Spectral Properties ◽  
Differential Operators ◽  
Second Order ◽  
Independent Interest ◽  
Compactly Supported ◽  
Compactly Supported Functions

In the paper, we establish the oscillatory and spectral properties of a class of fourth-order differential operators in dependence on integral behavior of its coefficients at zero and infinity. In order to obtain these results, we investigate a certain weighted second-order differential inequality of independent interest.

scholarly journals ON THE NUMERICAL SIMULATION OF TIME-SPACE FRACTIONAL COUPLED NONLINEAR SCHRÖDINGER EQUATIONS UTILIZING WENDLAND’S COMPACTLY SUPPORTED FUNCTION COLLOCATION METHOD

2021 ◽  
Vol 26 (1) ◽  
pp. 94-115
Author(s):  
Bahar Karaman
Keyword(s):  
Fractional Derivatives ◽  
Von Neumann ◽  
Nonlinear Schrödinger ◽  
Compactly Supported ◽  
Time Space ◽  
Compactly Supported Function ◽  
Conformable Derivatives ◽  
The Stability ◽  
Compactly Supported Functions ◽  
Nicolson Scheme

This research describes an efficient numerical method based on Wendland’s compactly supported functions to simulate the time-space fractional coupled nonlinear Schrödinger (TSFCNLS) equations. Here, the time and space fractional derivatives are considered in terms of Caputo and Conformable derivatives, respectively. The present numerical discussion is based on the following ways: we first approximate the Caputo fractional derivative of the proposed equation by a scheme order O(∆t2−α), 0 < α < 1 and then the Crank-Nicolson scheme is employed in the mentioned equation to discretize the equations. Second, applying a linear difference scheme to avoid solving nonlinear systems. In this way, we have a linear, suitable calculation scheme. Then, the conformable fractional derivatives of the Wendland’s compactly supported functions are established for the scheme. The stability analysis of the suggested scheme is also examined in a similar way to the classic Von-Neumann technique for the governing equations. The efficiency and accuracy of the present method are verified by solving two examples.

scholarly journals Density and trace results in generalized fractal networks

2018 ◽  
Vol 52 (3) ◽  
pp. 1023-1049
Author(s):  
Serge Nicaise ◽  
Adrien Semin
Keyword(s):  
Sobolev Space ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Trace Operator ◽  
Compactly Supported ◽  
Weighted Trees ◽  
Compactly Supported Functions ◽  
Necessary And Sufficient

The first aim of this paper is to give different necessary and sufficient conditions that guarantee the density of the set of compactly supported functions into the Sobolev space of order one in infinite p-adic weighted trees. The second goal is to define properly a trace operator in this Sobolev space if it makes sense.

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