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On Some Degenerate Differential Operators on Weighted Function Spaces

✍ Scribed by Francesco Altomare; Ingrid Carbone

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
302 KB
Volume
213
Category
Article
ISSN
0022-247X

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✦ Synopsis

We deal with the degenerate differential operator Au x [ ␣ x uЉ x xG0

Here W denotes the Banach space of all

w w Moreover, we assume that the function ␣ is continuous and positive on 0, qϱ , it Ž . Ž . is differentiable at 0, and satisfies the inequalities 0

for suitable constants ␣ and ␣ . We show that the operator A generates a 0 1 Ž Ž .. 0 C -semigroup T t of positive operators on W . Moreover, we prove that 0 t G 0 2

Ž . every T t can be represented as a limit of powers of suitable discrete-type positive linear operators that are constructed by means of the coefficient ␣. ᮊ 1997

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