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Unique continuation for Schrödinger operators with potential in Morrey spaces.

Alberto Ruiz, Luis Vega (1991)

Publicacions Matemàtiques

Let us consider in a domain Ω of Rn solutions of the differential inequality|Δu(x)| ≤ V(x)|u(x)|, x ∈ Ω,where V is a non smooth, positive potential.We are interested in global unique continuation properties. That means that u must be identically zero on Ω if it vanishes on an open subset of Ω.

Unique prime factorization in a partial semigroup of matrix-polynomials

Michael Kaltenbäck, Harald Woracek (2006)

Discussiones Mathematicae - General Algebra and Applications

We establish a unique factorization result into irreducibel elements in the partial semigroup of 2 × 2-matrices with entries in K[x] whose determinant is equal to 1, where K is a field, and where multiplication is defined as the usual matrix-multiplication if the degrees of the factors add up. This investigation is motivated by a result on matrices of entire functions.

Unitaires multiplicatifs en dimension finie et leurs sous-objets

Saad Baaj, Étienne Blanchard, Georges Skandalis (1999)

Annales de l'institut Fourier

On appelle pré-sous-groupe d’un unitaire multiplicatif V agissant sur un espace hilbertien de dimension finie une droite vectorielle L de telle que V ( L L ) = L L . Nous montrons que les pré-sous-groupes sont en nombre fini, donnons un équivalent du théorème de Lagrange et généralisons à ce cadre la construction du “bi-produit croisé”. De plus, nous établissons des bijections entre pré-sous-groupes et sous-algèbres coïdéales de l’algèbre de Hopf associée à V , et donc, d’après Izumi, Longo, Popa, avec les...

Unital strongly harmonic commutative Banach algebras

Janko Bračič (2002)

Studia Mathematica

A unital commutative Banach algebra is spectrally separable if for any two distinct non-zero multiplicative linear functionals φ and ψ on it there exist a and b in such that ab = 0 and φ(a)ψ(b) ≠ 0. Spectrally separable algebras are a special subclass of strongly harmonic algebras. We prove that a unital commutative Banach algebra is spectrally separable if there are enough elements in such that the corresponding multiplication operators on have the decomposition property (δ). On the other hand,...

Unitary asymptotes of Hilbert space operators

László Kérchy (1994)

Banach Center Publications

In this survey article we are going to present the effectiveness of the use of unitary asymptotes in the study of Hilbert space operators.

Unitary dilation for polar decompositions of p-hyponormal operators

Muneo Chō, Tadasi Huruya, Kôtarô Tanahashi (2005)

Banach Center Publications

In this paper, we introduce the angular cutting and the generalized polar symbols of a p-hyponormal operator T in the case where U of the polar decomposition T = U|T| is not unitary and study spectral properties of it.

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