scholarly journals Semilinear pseudodifferential equations in spaces of tempered ultradistributions

2016 ◽  
Vol 442 (1) ◽  
pp. 317-338 ◽  
Author(s):  
Marco Cappiello ◽  
Stevan Pilipović ◽  
Bojan Prangoski
Keyword(s):  
Pseudodifferential Equations ◽  
Tempered Ultradistributions

UNIFORMLY ASYMPTOTIC SOLUTIONS FOR PSEUDODIFFERENTIAL EQUATIONS WITH SINGULAR INTEGRAL OPERATORS

2001 ◽  
Vol 09 (02) ◽  
pp. 495-513 ◽  
Author(s):  
A. HANYGA ◽  
M. SEREDYŃSKA
Keyword(s):  
Asymptotic Solution ◽  
Frequency Domain ◽  
Singular Integral ◽  
Hyperbolic Equations ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Asymptotic Solutions ◽  
Convolution Operators ◽  
Pseudodifferential Equations

Uniformly asymptotic frequency-domain solutions for a class of hyperbolic equations with singular convolution operators are derived. Asymptotic solutions for this class of equations involve additional parameters — called attenuation parameters — which control the smoothing of the wavefield at the wavefront. At caustics the ray amplitudes have a singularity associated with vanishing of ray spreading and with divergence of an integral controlling the rate of exponential amplitude decay. Both problems are resolved by applying a generalized Kravtsov–Ludwig formula derived in this paper. A different asymptotic solution is constructed in the case of separation of dispersion and focusing effects.

scholarly journals Characterization of Wave Fronts of Ultradistributions Using Directional Short-Time Fourier Transform

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 240
Author(s):  
Sanja Atanasova ◽  
Snježana Maksimović ◽  
Stevan Pilipović
Keyword(s):  
Fourier Transform ◽  
Wave Front ◽  
Short Time Fourier Transform ◽  
Wave Fronts ◽  
Directional Wave ◽  
Tempered Ultradistributions ◽  
Short Time

In this paper we give a characterization of Sobolev k-directional wave front of order p∈[1,∞) of tempered ultradistributions via the directional short-time Fourier transform.

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