Summary: REMARKS ON RESTRICTION EIGENFUNCTIONS IN CN
GABRIELA PUTINAR AND MIHAI PUTINAR
To Ed Saff on the occasion of his 60-th birthday
Abstract. An elementary inquiry, based on examples and counterexamples, of some qualitative
properties of doubly orthogonal systems of analytic functions on domains in Cn leads to a better
understanding of the deviation from the classical Hardy space of the disk setting. The main results
relay on Hilbert space with reproducing kernel techniques.
Key words. Hilbert space with reproducing kernel, restriction operator, doubly orthogonal
system, min-max principle.
AMS subject classifications. 47A75, 32A25, 65F15
Department of Mathematics, University of California, Santa Barbara, CA 93106, gputinar-
Department of Mathematics, University of California, Santa Barbara, CA 93106, mputinar-
1. Introduction. Let be a bounded domain of Cn
and let H() be a Hilbert
space of analytic functions defined on , with reproducing kernel
K(z, w) = kw, kz , z, w .