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Displaying similar documents to “On L w 2 -quasi-derivatives for solutions of perturbed general quasi-differential equations”

On quadratically integrable solutions of the second order linear equation

T. Chantladze, Nodar Kandelaki, Alexander Lomtatidze (2001)

Archivum Mathematicum

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Integral criteria are established for dim V i ( p ) = 0 and dim V i ( p ) = 1 , i ∈ { 0 , 1 } , where V i ( p ) is the space of solutions u of the equation u ' ' + p ( t ) u = 0 satisfying the condition ∫ + ∞ u 2 ( s ) s i d s < + ∞ .

Fine and quasi connectedness in nonlinear potential theory

David R. Adams, John L. Lewis (1985)

Annales de l'institut Fourier

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If B α , p denotes the Bessel capacity of subsets of Euclidean n -space, α &gt; 0 , 1 &lt; p &lt; ∞ , naturally associated with the space of Bessel potentials of L p -functions, then our principal result is the estimate: for 1 &lt; α p ≤ n , there is a constant C = C ( α , p , n ) such that for any set E min { B α , p ( E ∩ Q ) , B α , p ( E c ∩ Q ) } ≤ C · B α , p ( Q ∩ ∂ f E ) for all open cubes Q in n -space. Here ∂ f E is the boundary of the E in the ( α , p ) -fine topology i.e. the smallest topology on c -space that makes the associated ( α , p ) -linear potentials continuous there. As a consequence,...

Quasi-constricted linear operators on Banach spaces

Eduard Yu. Emel&amp;#039;yanov, Manfred P. H. Wolff (2001)

Studia Mathematica

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Let X be a Banach space over ℂ. The bounded linear operator T on X is called quasi-constricted if the subspace X ₀ : = x ∈ X : l i m n → ∞ | | T ⁿ x | | = 0 is closed and has finite codimension. We show that a power bounded linear operator T ∈ L(X) is quasi-constricted iff it has an attractor A with Hausdorff measure of noncompactness χ | | · | | ₁ ( A ) < 1 for some equivalent norm ||·||₁ on X. Moreover, we characterize the essential spectral radius of an arbitrary bounded operator T by quasi-constrictedness of scalar multiples of T. Finally, we prove...

On quasi-compactness of operator nets on Banach spaces

Eduard Yu. Emel&#039;yanov (2011)

Studia Mathematica

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The paper introduces a notion of quasi-compact operator net on a Banach space. It is proved that quasi-compactness of a uniform Lotz-Räbiger net ( T λ ) λ is equivalent to quasi-compactness of some operator T λ . We prove that strong convergence of a quasi-compact uniform Lotz-Räbiger net implies uniform convergence to a finite-rank projection. Precompactness of operator nets is also investigated.

Representation and construction of homogeneous and quasi-homogeneous n -ary aggregation functions

Yong Su, Radko Mesiar (2021)

Kybernetika

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Homogeneity, as one type of invariantness, means that an aggregation function is invariant with respect to multiplication by a constant, and quasi-homogeneity, as a relaxed version, reflects the original output as well as the constant. In this paper, we characterize all homogeneous/quasi-homogeneous n -ary aggregation functions and present several methods to generate new homogeneous/quasi-homogeneous n -ary aggregation functions by aggregation of given ones.

Some remarks on quasi-Cohen sets

Pascal Lefèvre, Daniel Li (2001)

Colloquium Mathematicae

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We are interested in Banach space geometry characterizations of quasi-Cohen sets. For example, it turns out that they are exactly the subsets E of the dual of an abelian compact group G such that the canonical injection C ( G ) / C E c ( G ) ↪ L ² E ( G ) is a 2-summing operator. This easily yields an extension of a result due to S. Kwapień and A. Pełczyński. We also investigate some properties of translation invariant quotients of L¹ which are isomorphic to subspaces of L¹.