Displaying similar documents to “Generalized Gaudin models and Riccatians”

Commuting linear operators and algebraic decompositions

Rod A. Gover, Josef Šilhan (2007)

Archivum Mathematicum

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For commuting linear operators P 0 , P 1 , ⋯ , P ℓ we describe a range of conditions which are weaker than invertibility. When any of these conditions hold we may study the composition P = P 0 P 1 ⋯ P ℓ in terms of the component operators or combinations thereof. In particular the general inhomogeneous problem P u = f reduces to a system of simpler problems. These problems capture the structure of the solution and range spaces and, if the operators involved are differential, then this gives an effective way of lowering the...

Differential calculus on almost commutative algebras and applications to the quantum hyperplane

Cătălin Ciupală (2005)

Archivum Mathematicum

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In this paper we introduce a new class of differential graded algebras named DG ρ -algebras and present Lie operations on this kind of algebras. We give two examples: the algebra of forms and the algebra of noncommutative differential forms of a  ρ -algebra. Then we introduce linear connections on a  ρ -bimodule M over a  ρ -algebra  A and extend these connections to the space of forms from A to M . We apply these notions to the quantum hyperplane.

A remark on a modified Szász-Mirakjan operator

Guanzhen Zhou, Songping Zhou (1999)

Colloquium Mathematicae

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We prove that, for a sequence of positive numbers δ(n), if n 1 / 2 δ ( n ) ¬ → ∞ as n → ∞ , to guarantee that the modified Szász-Mirakjan operators S n , δ ( f , x ) converge to f(x) at every point, f must be identically zero.

Oblique derivative problem for elliptic equations in non-divergence form with V M O coefficients

Giuseppe di Fazio, Dian K. Palagachev (1996)

Commentationes Mathematicae Universitatis Carolinae

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A priori estimates and strong solvability results in Sobolev space W 2 , p ( Ω ) , 1 < p < ∞ are proved for the regular oblique derivative problem ∑ i , j = 1 n a i j ( x ) ∂ 2 u ∂ x i ∂ x j = f ( x ) a.e. Ω ∂ u ∂ ℓ + σ ( x ) u = ϕ ( x ) on ∂ Ω when the principal coefficients a i j are V M O ∩ L ∞ functions.

Examples of functions -extendable for each finite, but not ∞ -extendable

Wiesław Pawłucki (1998)

Banach Center Publications

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In Example 1, we describe a subset X of the plane and a function on X which has a k -extension to the whole ℝ 2 for each finite, but has no ∞ -extension to ℝ 2 . In Example 2, we construct a similar example of a subanalytic subset of ℝ 5 ; much more sophisticated than the first one. The dimensions given here are smallest possible.

Two Families of Self-adjoint Indecomposable Operators in an Orthomodular Space

Carla Barrios Rodríguez (2008)

Annales mathématiques Blaise Pascal

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Orthomodular spaces are the counterpart of Hilbert spaces for fields other than ℝ or ℂ . Both share numerous properties, foremost among them is the validity of the Projection theorem. Nevertheless in the study of bounded linear operators which started in [], there appeared striking differences with the classical theory. In fact, in this paper we shall construct, on the canonical non-archimedean orthomodular space E of [], two infinite families of self-adjoint bounded linear operators...