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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.

Zeroes of the Bergman kernel of Hartogs domains

Miroslav Engliš (2000)

Commentationes Mathematicae Universitatis Carolinae

We exhibit a class of bounded, strongly convex Hartogs domains with real-analytic boundary which are not Lu Qi-Keng, i.e. whose Bergman kernel function has a zero.

Zeros of bounded holomorphic functions in strictly pseudoconvex domains in 2

Jim Arlebrink (1993)

Annales de l'institut Fourier

Let D be a bounded strictly pseudoconvex domain in 2 and let X be a positive divisor of D with finite area. We prove that there exists a bounded holomorphic function f such that X is the zero set of f . This result has previously been obtained by Berndtsson in the case where D is the unit ball in 2 .

Zeta functions and blow-Nash equivalence

Goulwen Fichou (2005)

Annales Polonici Mathematici

We propose a refinement of the notion of blow-Nash equivalence between Nash function germs, which has been introduced in [2] as an analog in the Nash setting of the blow-analytic equivalence defined by T.-C. Kuo [13]. The new definition is more natural and geometric. Moreover, this equivalence relation still does not admit moduli for a Nash family of isolated singularities. But though the zeta functions constructed in [2] are no longer invariants for this new relation, thanks to a Denef & Loeser...

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