scholarly journals Boundedness of pseudo‐differential operators of type (0,0) on Triebel–Lizorkin and Besov spaces

2019 ◽  
Vol 51 (6) ◽  
pp. 1039-1060 ◽  
Author(s):  
Bae Jun Park
Keyword(s):  
Besov Spaces ◽  
Differential Operators ◽  
Pseudo Differential Operators

On the continuity of pseudo-differential operators on Besov spaces

Analysis ◽  
2006 ◽  
Vol 26 (4) ◽  
Author(s):  
Madani Moussai
Keyword(s):  
Besov Space ◽  
Besov Spaces ◽  
Differential Operators ◽  
Positive Real ◽  
Pseudo Differential Operators

We study the continuity of pseudo-differential operators on Besov spacefor some positive real

scholarly journals DIFFRACTION BY A UNION OF STRIPS WITH IMPEDANCE CONDITIONS IN BESOV AND BESSEL POTENTIAL SPACES

2008 ◽  
Vol 13 (2) ◽  
pp. 183-194
Author(s):  
Luis P. Castro ◽  
David Kapanadze
Keyword(s):  
Wave Diffraction ◽  
Besov Spaces ◽  
Differential Operators ◽  
Diffraction Problem ◽  
Bessel Potential ◽  
Impedance Boundary ◽  
Pseudo Differential Operators ◽  
Impedance Parameters ◽  
Impedance Conditions ◽  
Bessel Potential Spaces

We consider an impedance boundary‐value problem for the Helmholtz equation which models a wave diffraction problem with imperfect conductivity on a union of strips. Pseudo‐differential operators acting between Bessel potential spaces and Besov spaces are used to deal with this wave diffraction problem. In particular, these operators allow a reformulation of the problem into a system of integral equations. The main result presents impedance parameters which ensure the well-posedness of the problem in scales of Bessel potential spaces and Besov spaces.

scholarly journals A Radial Basis Function Finite Difference Scheme for the Benjamin–Ono Equation

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 65
Author(s):  
Benjamin Akers ◽  
Tony Liu ◽  
Jonah Reeger
Keyword(s):  
Radial Basis Function ◽  
Hilbert Transform ◽  
Basis Function ◽  
Differential Operators ◽  
Convergence Rates ◽  
Traveling Wave Solutions ◽  
Algebraic Decay ◽  
Pseudo Differential Operators ◽  
Radial Basis ◽  
The Hilbert Transform

A radial basis function-finite differencing (RBF-FD) scheme was applied to the initial value problem of the Benjamin–Ono equation. The Benjamin–Ono equation has traveling wave solutions with algebraic decay and a nonlocal pseudo-differential operator, the Hilbert transform. When posed on R, the former makes Fourier collocation a poor discretization choice; the latter is challenging for any local method. We develop an RBF-FD approximation of the Hilbert transform, and discuss the challenges of implementing this and other pseudo-differential operators on unstructured grids. Numerical examples, simulation costs, convergence rates, and generalizations of this method are all discussed.

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