Hilbert–Schimdt and Trace Class Pseudo-Differential Operators and Weyl Transforms on the Affine Group

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Aparajita Dasgupta ◽  
Santosh Kumar Nayak ◽  
M. W. Wong
Keyword(s):  
Differential Operators ◽  
Trace Class ◽  
Affine Group ◽  
Pseudo Differential Operators ◽  
Weyl Transforms

scholarly journals On the Weyl transform for rotationally invariant symbols

2019 ◽  
Vol 10 (4) ◽  
pp. 769-791 ◽  
Author(s):  
Norbert Ortner ◽  
Peter Wagner
Keyword(s):  
Asymptotic Behavior ◽  
Differential Operators ◽  
Symmetric Distributions ◽  
Yield Criteria ◽  
Weyl Transform ◽  
Pseudo Differential Operators ◽  
Weyl Transforms ◽  
Rotationally Invariant

Abstract Several formulas for the eigenvalues $$\lambda _j$$ λ j of the Weyl transforms $$W_\sigma $$ W σ of symbols $$\sigma $$ σ given by radially symmetric distributions are derived. These yield criteria for the boundedness and the compactness, respectively, of the pseudo-differential operators $$W_\sigma .$$ W σ . We investigate some examples by analyzing the asymptotic behavior of $$\lambda _j$$ λ j for $$j\rightarrow \infty $$ j → ∞ .

scholarly journals Pseudo-differential operators on homogeneous spaces of compact and Hausdorff groups

2019 ◽  
Vol 31 (2) ◽  
pp. 275-282 ◽  
Author(s):  
Vishvesh Kumar
Keyword(s):  
Homogeneous Space ◽  
Closed Subgroup ◽  
Differential Operators ◽  
Homogeneous Spaces ◽  
Trace Class ◽  
Necessary And Sufficient Condition ◽  
Pseudo Differential Operators ◽  
Hausdorff Group ◽  
Necessary And Sufficient

AbstractLet G be a compact Hausdorff group and let H be a closed subgroup of G. We introduce pseudo-differential operators with symbols on the homogeneous space {G/H}. We present a necessary and sufficient condition on symbols for which these operators are in the class of Hilbert–Schmidt operators. We also give a characterization of and a trace formula for the trace class pseudo-differential operators on the homogeneous space {G/H}.

Weyl transforms and a degenerate elliptic partial differential equation

2005 ◽  
Vol 461 (2064) ◽  
pp. 3863-3870 ◽  
Author(s):  
M.W Wong
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Differential Operators ◽  
Partial Differential Operator ◽  
Elliptic Partial Differential Equation ◽  
Hermite Functions ◽  
Partial Differential ◽  
Pseudo Differential Operators ◽  
Weyl Transforms ◽  
Degenerate Elliptic

We give a formula for the inverse of a degenerate elliptic partial differential operator P on related to the Heisenberg group. The formula is in terms of pseudo-differential operators of the Weyl type, i.e. Weyl transforms. The technique is to use the Fourier–Wigner transforms of Hermite functions, which form an orthonormal basis for . Using the formula for the inverse, we give an estimate for the L p norm of the solution u of the partial differential equation Pu = f on in terms of the L 2 norm of f , 2≤ p ≤∞.

Pseudo-differential operators involving Fractional Fourier cosine (sine) transform

Filomat ◽  
2017 ◽  
Vol 31 (6) ◽  
pp. 1791-1801
Author(s):  
Akhilesh Prasad ◽  
Manoj Singh
Keyword(s):  
Differential Operators ◽  
Fourier Cosine ◽  
Sine Transform ◽  
Pseudo Differential Operators
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