# Wydawnictwa / Czasopisma IMPAN / Annales Polonici Mathematici / Wszystkie zeszyty

## An extension theorem with analytic singularities for generalized $(N,k)$-crosses

### Tom 103 / 2012

Annales Polonici Mathematici 103 (2012), 193-208 MSC: Primary 32D15; Secondary 32D10. DOI: 10.4064/ap103-2-7

#### Streszczenie

The main result of the paper is a new Hartogs type extension theorem for generalized $(N,k)$-crosses with analytic singularities for separately holomorphic functions and for separately meromorphic functions. Our result is a simultaneous generalization of several known results, from the classical cross theorem, through the extension theorem with analytic singularities for generalized crosses, to the cross theorem with analytic singularities for meromorphic functions.