SELF-SIMILAR DRUMS AND GENERALIZED WEIERSTRASS FUNCTIONS

Autor(en): GERLING, J
SCHMIDT, HJ
Stichwörter: Physics; Physics, Multidisciplinary
Erscheinungsdatum: 1992
Herausgeber: ELSEVIER SCIENCE BV
Journal: PHYSICA A
Volumen: 191
Ausgabe: 1-4
Startseite: 536
Seitenende: 539
Zusammenfassung: 
We consider the number N(lambda; OMEGA) of eigenvalues less than A of the negative Laplacian with Dirichlet boundary conditions in a domain OMEGA subset-of R(n) with fractal boundary partial derivative OMEGA. It is known that for lambda --> infinity, N(lambda; OMEGA) = C(n)OMEGAn lambda(n/2) O(lambda(D/2)), where D is the Minkowski dimension of OMEGA. For a certain class of self-similar domains (''drums'') we obtain for N(lambda; OMEGA) a second term of the form -F(In lambda)lambda(D/2) with a bounded periodic function F. F contains a generalized Weierstrass function with a self-similar fractal graph. A number of examples with n = 1, 2, 3, . . . has been studied, where more information about F is available. Finally, a possible physical application will be sketched.
Beschreibung: 
INTERNATIONAL CONF ON FRACTALS AND DISORDERED SYSTEMS, UNIV HAMBURG, HAMBURG, GERMANY, JUL 29-31, 1992
ISSN: 03784371
DOI: 10.1016/0378-4371(92)90578-E

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