The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Page 1

Displaying 1 – 17 of 17

Showing per page

On extensions of holomorphic functions satisfying a polynomial growth condition on algebraic varieties in 𝐂 n

Jean Erik Björk (1974)

Annales de l'institut Fourier

Let V be an algebraic variety in C n and when k 0 is an integer then Pol ( V , k ) denotes all holomorphic functions f ( z ) on V satisfying | f ( z ) | C f ( 1 + | z | ) k for all z V and some constant C f . We estimate the least integer ϵ ( V , k ) such that every f Pol ( V , k ) admits an extension from V into C n by a polynomial P ( z 1 , ... , z n ) , of degree k + ϵ ( V , k ) at most. In particular lim k > ϵ ( V , k ) is related to cohomology groups with coefficients in coherent analytic sheaves on V . The existence of the finite integer ϵ ( V , k ) is for example an easy consequence of Kodaira’s Vanishing Theorem.

Currently displaying 1 – 17 of 17

Page 1