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Generalized Second Order Differential Operators

✍ Scribed by J.-U. Löbus

Publisher
John Wiley and Sons
Year
1991
Tongue
English
Weight
615 KB
Volume
152
Category
Article
ISSN
0025-584X

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📜 SIMILAR VOLUMES

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## Abstract Generalized second order differential operators of the form $ {d \over {d \mu}} {d \over {dx}} $ when __μ__ is a selfsimilar measure whose support is the classical Cantor set are considered. The asymptotic distribution of the zeros of the eigenfunctions is determined. (© 2004 WILEY‐VCH

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We deal with the problem of analyticity for the semigroup generated by the second order differential operator Au := αu + βu (or by some restrictions of it) in the spaces L p (0, 1), with or without weight, and in W 1,p (0, 1), 1 < p < ∞. Here α and β are assumed real-valued and continuous in [0, 1],

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The existence of a unique 71 x n matrix spectral function is shown for a selfadjoint operator A in a Hilbert space Lg(m). This Hilbert space is a subspace of the product of spaces L2(rn;) with measures rn,, i = 1 , . . . , n , having support i n [O,m). The inner product in Li(m) is the weighted sum