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Weighted sub-Bergman Hilbert spaces

Maria Nowak, Renata Rososzczuk (2014)

Annales UMCS, Mathematica

We consider Hilbert spaces which are counterparts of the de Branges-Rovnyak spaces in the context of the weighted Bergman spaces A2α, −1 < α < ∞. These spaces have already been studied in [8], [7], [5] and [1]. We extend some results from these papers

Weighted sub-Bergman Hilbert spaces in the unit disk

Ali Abkar, B. Jafarzadeh (2010)

Czechoslovak Mathematical Journal

We study sub-Bergman Hilbert spaces in the weighted Bergman space A α 2 . We generalize the results already obtained by Kehe Zhu for the standard Bergman space A 2 .

Wiener-Hopf integral operators with PC symbols on spaces with Muckenhoupt weight.

Albrecht Böttcher, Ilya M. Spitkovsky (1993)

Revista Matemática Iberoamericana

We describe the spectrum and the essential spectrum and give an index formula for Wiener-Hopf integral operators with piecewise continuous symbols on the space Lp(R+,ω) with a Muckenhoupt weight ω. Our main result says that the essential spectrum is a set resulting from the essential range of the symbol by joining the two endpoints of each jump by a certain sickle-shaped domain, whose shape is completely determined by the value of p and the behavior of the weight ω at the origin and at infinity.

Zero sums of products of Toeplitz and Hankel operators on the Hardy space

Young Joo Lee (2015)

Studia Mathematica

On the Hardy space of the unit disk, we consider operators which are finite sums of products of a Toeplitz operator and a Hankel operator. We then give characterizations for such operators to be zero. Our results extend several known results using completely different arguments.

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