Premium
Zwei Klassen vollständiger Funktionensysteme zur Behandlung der Randwertaufgaben der Schwingungsgleichung Δ U + k 2 U = 0
Author(s) -
Müller C.,
Kersten H.,
Leis R.
Publication year - 1980
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670020106
Subject(s) - mathematics , singularity , basis (linear algebra) , norm (philosophy) , dirichlet distribution , pure mathematics , mathematical analysis , boundary value problem , geometry , political science , law
In this paper we present new methods to solve the classical Dirichlet and Neumann problems for Δ U + k 2 U = 0. We prove that the solutions of this equation for a region S containing G restricted to G are dense in L 2 (∂ G ). Introducing a basis in the space of solutions for S we find a complete orthogonal system in L 2 (∂ G ) which can be used to solve the boundary value problems by means of approximation in the Hilbertspace norm. Regularity estimates lead to series expansions in G . The well‐known basis systems obtained by separation of variables thus may be used for every regular region without the very special geometric restrictions. Another class of basis systems may be obtained in analogy to the Runge. theorems by considering types of singularity functions.