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A remark on complex powers of analytic functions

Giuseppe Zampieri (1985)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Sia K n un compatto, f 0 una funzione analitica all'intorno di K , ed m la massima molteplicità in K degli zeri di f ; si prova che la potenza f λ ( λ , R e λ > 1 m ) è integrabile in K . L'estensione meromorfa dell'applicazione λ f λ da R e λ > 0 a tutto (con valori in 𝒟 ( K ) anziché in L 1 ( K ) ) era già stata provata in [1] e [2].

A remark on Nilsson type integrals

Nguyen Minh, Bogdan Ziemian (1996)

Banach Center Publications

We investigate ramification properties with respect to parameters of integrals (distributions) of a class of singular functions over an unbounded cycle which may intersect the singularities of the integrand. We generalize the classical result of Nilsson dealing with the case where the cycle is bounded and contained in the set of holomorphy of the integrand. Such problems arise naturally in the study of exponential representation at infinity of solutions to certain PDE's (see [Z]).

A remark on separate holomorphy

Marek Jarnicki, Peter Pflug (2006)

Studia Mathematica

Let X be a Riemann domain over k × . If X is a domain of holomorphy with respect to a family ℱ ⊂(X), then there exists a pluripolar set P k such that every slice X a of X with a∉ P is a region of holomorphy with respect to the family f | X a : f .

A remark on the identity principle for analytic sets

Marek Jarnicki, Peter Pflug (2011)

Colloquium Mathematicae

We present a version of the identity principle for analytic sets, which shows that the extension theorem for separately holomorphic functions with analytic singularities follows from the case of pluripolar singularities.

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