LANGER, H and MENNICKEN, R and MOLLER, M (1993) EXPANSION OF ANALYTIC-FUNCTIONS IN SERIES OF FLOQUET SOLUTIONS OF 1ST-ORDER DIFFERENTIAL-SYSTEMS. MATHEMATISCHE NACHRICHTEN, 162. pp. 279-314. ISSN 0025-584X, 1522-2616
Full text not available from this repository.Abstract
In this paper we study boundary eigenvalue problems for first order systems of ordinary differential equations of the form zy'(z) = (lambdaA1(z) + A0(z)) y(z), y(ze2pii) = e(2piinu)y(z) for z is-an-element-of S(log), where S is a ring region around zero, S(log) denotes the Riemann surface of the logarithm over S, the coefficient matrix functions A1(z) and A0(z) are holomorphic on S, and nu is a complex number. The eigenfunctions of this eigenvalue problem are the Floquet solutions of the differential system with nu as characteristic exponent. For an open subset S0 of S, the notion of A1-convexity of the pair (S0, S) is introduced. For A1-convex pairs (S0, S) it is shown that the expansion into eigenfunctions and associated functions of holomorphic functions on S(log), satisfying the monodromy condition y(ze2pii) = e(2piinu)y(z), converges regularly on S0log and is unique. If S is a pointed neighbourhood of 0 and A1(z) is holomorphic in S or {0}, it is shown that there is a pointed neighbourhood S0 of 0 such that (S0, S) is A1-convex. It follows from the results of this paper that many expansions of analytic functions in terms of special functions can be considered as eigenfunction expansions of this kind.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ; |
| Depositing User: | Dr. Gernot Deinzer |
| Last Modified: | 19 Oct 2022 08:43 |
| URI: | https://pred.uni-regensburg.de/id/eprint/54203 |
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