Stein–Weiss Operators and Ellipticity
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TLDR
In this paper, Stein and Weiss introduced the notion of generalized gradients and proved ellipticity for certain systems, analogous to the Cauchy Riemann equations and to the (Riemannian signature) Maxwell and Dirac equations.About:
This article is published in Journal of Functional Analysis.The article was published on 1997-12-15 and is currently open access. It has received 110 citations till now. The article focuses on the topics: Clifford analysis & Dirac operator.read more
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Conformal Killing forms on Riemannian manifolds
TL;DR: Conformal Killing Fields as mentioned in this paper are a generalization of conformal vector fields on Riemannian manifolds, defined as sections in the kernel of a conformally invariant first order differential operator.
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Conformal Killing forms on Riemannian manifolds
TL;DR: Conformal Killing Fields as mentioned in this paper are a generalization of conformal vector fields on Riemannian manifolds, defined as sections in the kernel of a conformally invariant first order differential operator.
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Refined Kato inequalities and conformal weights in Riemannian geometry
TL;DR: In this article, the authors established refinements of the classical Kato inequality for sections of a vector bundle which lie in the kernel of a natural injectively elliptic first-order linear differential operator.
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Conformally covariant differential operators: properties and applications
TL;DR: In this paper, conformally covariant differential operators, which under local rescalings of the metric, transform according to for some r if is of order s, are discussed. And the flat space restrictions of their associated Green functions have forms which are strongly constrained by flat space conformal invariance.
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Killing and conformal Killing tensors
TL;DR: In this paper, an appropriate formalism was introduced in order to study conformal Killing (symmetric) tensors on Riemannian manifolds and several new results were obtained.
References
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Partial Differential Equations
TL;DR: In this paper, the authors present a theory for linear PDEs: Sobolev spaces Second-order elliptic equations Linear evolution equations, Hamilton-Jacobi equations and systems of conservation laws.
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Graduate Texts in Mathematics
Rajendra Bhatia,Glen Bredon,Wolfgang Walter,Joseph J. Rotman,M. Ram Murty,Jane Gilman,Peter Walters,Martin Golubitsky,Ioannis Karatzas,Henri Cohen,Raoul Bott,Gaisi Takeuti,Béla Bollobás,John M. Lee,Jiří Matoušek,Saunders Mac Lane,John L. Kelley,B. A. Dubrovin,Tom M. Apostol,John Stillwell,William Arveson +20 more
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Intertwining Operators for Semisimple Groups, II
TL;DR: In this article, the authors extended the use of intertwining operators for semisimple Lie groups and showed that they can be used to determine the degree of reducibility of all series of representations appearing in the Plancherel formula of the group, and to study complementary series attached to them.