On Fredholm eigenvalue problem for plane domains
Nobuyuki Suita · Kodai Mathematical Journal · 1961
BY NOBUYUKI SUITA 1. Fredholm eigen value problem was mostly investigated in the case of basic domains bounded by a finite number of sufficiently smooth curves ([2],[4], [5]).Recently Ozawa dealt with the problem for a general domain ([3]).In the present paper we shall derive some properties of basic domains with special eigen values.2. We now explain the notations.Let D be a planar domain and L 2 (D) a Hubert space consisting of all analytic functions with finite norm and singlevalued indefinite integral.Here the inner product and norm are defined by (/, 9) = \\ fgdτ and