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Displaying similar documents to “Holomorphic subordinated semigroups”

Continuous selections on spaces of continuous functions

Angel Tamariz-Mascarúa (2006)

Commentationes Mathematicae Universitatis Carolinae

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For a space Z , we denote by ( Z ) , 𝒦 ( Z ) and 2 ( Z ) the hyperspaces of non-empty closed, compact, and subsets of cardinality 2 of Z , respectively, with their Vietoris topology. For spaces X and E , C p ( X , E ) is the space of continuous functions from X to E with its pointwise convergence topology. We analyze in this article when ( Z ) , 𝒦 ( Z ) and 2 ( Z ) have continuous selections for a space Z of the form C p ( X , E ) , where X is zero-dimensional and E is a strongly zero-dimensional metrizable space. We prove that C p ( X , E ) is weakly orderable...

Methods of analysis of the condition for correct solvability in L p ( ) of general Sturm-Liouville equations

Nina A. Chernyavskaya, Leonid A. Shuster (2014)

Czechoslovak Mathematical Journal

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We consider the equation - ( r ( x ) y ' ( x ) ) ' + q ( x ) y ( x ) = f ( x ) , x ( * ) where f L p ( ) , p ( 1 , ) and r > 0 , q 0 , 1 r L 1 loc ( ) , q L 1 loc ( ) , lim | d | x - d x d t r ( t ) · x - d x q ( t ) d t = . In an earlier paper, we obtained a criterion for correct solvability of ( * ) in L p ( ) , p ( 1 , ) . In this criterion, we use values of some auxiliary implicit functions in the coefficients r and q of equation ( * ). Unfortunately, it is usually impossible to compute values of these functions. In the present paper we obtain sharp by order, two-sided estimates (an estimate of a function f ( x ) for x ( a , b ) through a function g ( x ) is sharp by order if c - 1 | g ( x ) | | f ( x ) | c | g ( x ) | , ...