On the spectral synthesis in the spaces of solutions of invariant differential equations

1986 ◽  
pp. 85-100 ◽  
Author(s):  
P. A. Kuchment
Keyword(s):  
Differential Equations ◽  
Spectral Synthesis ◽  
Invariant Differential

A Tensor Equation of Elliptic Type

1953 ◽  
Vol 5 ◽  
pp. 524-535 ◽  
Author(s):  
G. F. D. Duff
Keyword(s):  
Riemannian Manifold ◽  
Differential Equations ◽  
Tensor Field ◽  
Differential Operators ◽  
Elliptic Type ◽  
Tensor Equation ◽  
Tensor Theory ◽  
Elliptic Differential Equations ◽  
Invariant Differential ◽  
Image Position

The theory of the systems of partial differential equations which arise in connection with the invariant differential operators on a Riemannian manifold may be developed by methods based on those of potential theory. It is therefore natural to consider in the same context the theory of elliptic differential equations, in particular those which are self-adjoint. Some results for a tensor equation in which appears, in addition to the operator Δ of tensor theory, a matrix or double tensor field defined on the manifold, are here presented. The equation may be writtenin a notation explained below.

Harmonic Spinors on Hyperbolic Space

1993 ◽  
Vol 36 (3) ◽  
pp. 257-262 ◽  
Author(s):  
Pierre-Yves Gaillard
Keyword(s):  
Differential Equations ◽  
Symmetric Space ◽  
Representation Theory ◽  
Hyperbolic Space ◽  
Harmonic Functions ◽  
Short Note ◽  
Harmonic Forms ◽  
Semisimple Symmetric Space ◽  
Invariant Differential ◽  
Harmonic Spinors

AbstractThe purpose for this short note is to describe the space of harmonic spinors on hyperbolicn-spaceHn. This is a natural continuation of the study of harmonic functions onHnin [Minemura] and [Helgason]—these results were generalized in the form of Helgason's conjecture, proved in [KKMOOT],—and of [Gaillard 1, 2], where harmonic forms onHnwere considered. The connection between invariant differential equations on a Riemannian semisimple symmetric spaceG/Kand homological aspects of the representation theory ofG, as exemplified in (8) below, does not seem to have been previously mentioned. This note is divided into three main parts respectively dedicated to the statement of the results, some reminders, and the proofs. I thank the referee for having suggested various improvements.

Synthesis of Discrete Filters by Invariant Differential Equations

2018 ◽  
Vol 3 (94) ◽  
pp. 10-16
Author(s):  
S. I. Ziatdinov ◽  
◽  
L. A. Osipov ◽  
Y. V. Sokolova ◽  
◽  
...  
Keyword(s):  
Differential Equations ◽  
Invariant Differential
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