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Displaying similar documents to “Higher order linear connections from first order ones”

Linear extensions of relations between vector spaces

Árpád Száz (2003)

Commentationes Mathematicae Universitatis Carolinae

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Let X and Y be vector spaces over the same field K . Following the terminology of Richard Arens [Pacific J. Math. 11 (1961), 9–23], a relation F of X into Y is called linear if λ F ( x ) F ( λ x ) and F ( x ) + F ( y ) F ( x + y ) for all λ K { 0 } and x , y X . After improving and supplementing some former results on linear relations, we show that a relation Φ of a linearly independent subset E of X into Y can be extended to a linear relation F of X into Y if and only if there exists a linear subspace Z of Y such that Φ ( e ) Y | Z for all e E . Moreover, if...

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 ) | , ...

A generalization of amenability and inner amenability of groups

Ali Ghaffari (2012)

Czechoslovak Mathematical Journal

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Let G be a locally compact group. We continue our work [A. Ghaffari: Γ -amenability of locally compact groups, Acta Math. Sinica, English Series, 26 (2010), 2313–2324] in the study of Γ -amenability of a locally compact group G defined with respect to a closed subgroup Γ of G × G . In this paper, among other things, we introduce and study a closed subspace A Γ p ( G ) of L ( Γ ) and then characterize the Γ -amenability of G using A Γ p ( G ) . Various necessary and sufficient conditions are found for a locally compact...