Approximation and symbolic calculus for Toeplitz algebras on the Bergman space.
Daniel Suárez (2004)
Revista Matemática Iberoamericana
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Daniel Suárez (2004)
Revista Matemática Iberoamericana
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Albrecht Böttcher, Sergei M. Grudsky, Enrique Ramírez de Arellano (2004)
Revista Matemática Iberoamericana
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This paper is devoted to Banach algebras generated by Toeplitz operators with strongly oscillating symbols, that is, with symbols of the form b[e] 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.
B. R. Choe, H. Koo, Y. J. Lee (2008)
Revista Matemática Iberoamericana
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Lucio Damascelli, Francesca Gladiali (2004)
Revista Matemática Iberoamericana
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Lidia Maniccia, Marco Mughetti (2006)
Revista Matemática Iberoamericana
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We prove Fefferman's SAK Principle for a class of hypoelliptic operators on R whose nonnegative symbol vanishes anisotropically on the characteristic manifold.
Loredana Lanzani, Osvaldo Méndez (2006)
Revista Matemática Iberoamericana
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Karlheinz Gröchenig (2006)
Revista Matemática Iberoamericana
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We investigate the properties an exotic symbol class of pseudodifferential operators, Sjöstrand's class, with methods of time-frequency analysis (phase space analysis). Compared to the classical treatment, the time-frequency approach leads to striklingly simple proofs of Sjöstrand's fundamental results and to far-reaching generalizations.
Gérard Bourdaud, Massimo Lanza de Cristoforis, Winfried Sickel (2006)
Revista Matemática Iberoamericana
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We characterize the set of all functions f of R to itself such that the associated superposition operator T: g → f º g maps the class BV (R) into itself. Here BV (R), 1 ≤ p < ∞, denotes the set of primitives of functions of bounded p-variation, endowed with a suitable norm. It turns out that such an operator is always bounded and sublinear. Also, consequences for the boundedness of superposition operators defined on Besov spaces B ...
Kyesook Nam, Dechao Zheng, Changyong Zhong (2006)
Revista Matemática Iberoamericana
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m-Berezin transforms are introduced for bounded operators on the Bergman space of the unit ball. The norm of the m-Berezin transform as a linear operator from the space of bounded operators to L is found. We show that the m-Berezin transforms are commuting with each other and Lipschitz with respect to the pseudo-hyperbolic distance on the unit ball. Using the m-Berezin transforms we show that a radial operator in the Toeplitz algebra is compact iff its Berezin transform vanishes on the...