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A Transmission Problem Involving a Parameter and a Weight
Author(s) -
Faierman M.
Publication year - 2001
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200109)229:1<73::aid-mana73>3.0.co;2-p
Subject(s) - mathematics , mathematical analysis , boundary value problem , transmission (telecommunications) , ordinary differential equation , transformation (genetics) , neighbourhood (mathematics) , partial differential equation , pure mathematics , differential equation , biochemistry , chemistry , electrical engineering , engineering , gene
In the course of developing a spectral theory for non‐selfadjoint elliptic boundary problems involving an indefinite weight function, there arises a transmission problem which has not hitherto been dealt with in a L p setting. By educing our problem to one for ordinary differential equations with the aid of the Fourier transformation, we are able to resolve the transmission problem,that is to say, we are able to establish L p estimates for its solutions which are supported in a neighbourhood of the origin, and this is p ecisely what is required for the furthe development of the spectral theory for the boundary problems cited above.