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Algebras of Toeplitz operators with oscillating symbols.

Albrecht Böttcher, Sergei M. Grudsky, Enrique Ramírez de Arellano (2004)

Revista Matemática Iberoamericana

This paper is devoted to Banach algebras generated by Toeplitz operators with strongly oscillating symbols, that is, with symbols of the form b[eia(x)] where b belongs to some algebra of functions on the unit circle and a is a fixed orientation-preserving homeomorphism of the real line onto itself. We prove the existence of certain interesting homomorphisms and establish conditions for the normal solvability, Fredholmness, and invertibility of operators in these algebras.

An integral formula of hyperbolic type for solutions of the Dirac equation on Minkowski space with initial conditions on a hyperboloid

Martin Sikora (2010)

Archivum Mathematicum

The Dirac equation for spinor-valued fields f on the Minkowski space of even dimension form a hyperbolic system of partial differential equations. In the paper, we are showing how to reconstruct the solution from initial data given on the upper sheet H + of the hyperboloid. In particular, we derive an integral formula expressing the value of f in a chosen point p as an integral over a compact cycle given by the intersection of the null cone with H + in the Minkowski space 𝕄 .

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