Displaying similar documents to “Inequalities for exponentials in Banach algebras”

On the joint spectral radius of commuting matrices

Rajendra Bhatia, Tirthankar Вhattacharyya (1995)

Studia Mathematica

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For a commuting n-tuple of matrices we introduce the notion of a joint spectral radius with respect to the p-norm and prove a spectral radius formula.

Characterizing spectra of closed operators through existence of slowly growing solutions of their Cauchy problems

Sen Huang (1995)

Studia Mathematica

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Let A be a closed linear operator in a Banach space E. In the study of the nth-order abstract Cauchy problem u ( n ) ( t ) = A u ( t ) , t ∈ ℝ, one is led to considering the linear Volterra equation (AVE) u ( t ) = p ( t ) + A ʃ 0 t a ( t - s ) u ( s ) d s , t ∈ ℝ, where a ( · ) L l o c 1 ( ) and p(·) is a vector-valued polynomial of the form p ( t ) = j = 0 n 1 / ( j ! ) x j t j for some elements x j E . We describe the spectral properties of the operator A through the existence of slowly growing solutions of the (AVE). The main tool is the notion of Carleman spectrum of a vector-valued function. Moreover, an extension...

On spectral representation for selfadjoint operators. Expansion in generalized eigenelements

Eberhard Gerlach (1965)

Annales de l'institut Fourier

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L’auteur reprend l’étude classique de la représentation spectrale d’un opérateur auto-adjoint A dans un espace de Hilbert . Il y ajoute des précisions nouvelles qui conduisent à la définition du projecteur infinitésimal P ) λ ) sur l’espace des vecteurs propres généralisés ( λ ) . Il obtient, par conséquent, des énoncés plus précis de bien des théorèmes classiques. Il introduit ensuite la notion de “ A -expansibilité” d’un sous-ensemble S . Cette notion est appliquée à l’étude des espaces fonctionnels...

The Weyl asymptotic formula by the method of Tulovskiĭ and Shubin

Paweł Głowacki (1998)

Studia Mathematica

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Let A be a pseudodifferential operator on N whose Weyl symbol a is a strictly positive smooth function on W = N × N such that | α a | C α a 1 - ϱ for some ϱ>0 and all |α|>0, α a is bounded for large |α|, and l i m w a ( w ) = . Such an operator A is essentially selfadjoint, bounded from below, and its spectrum is discrete. The remainder term in the Weyl asymptotic formula for the distribution of the eigenvalues of A is estimated. This is done by applying the method of approximate spectral projectors of Tulovskiĭ and Shubin. ...

Commutators associated to a subfactor and its relative commutants

Hsiang-Ping Huang (2002)

Annales de l’institut Fourier

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Let N M be an inclusion of I I 1 factors with finite Jones index. Then M = ( N ' M ) [ N , M ] as a vector space. Here [ N , M ] denotes the vector space spanned by the commutators of the form [ a , b ] where a N , b M .

Initial value problem for the time dependent Schrödinger equation on the Heisenberg group

Jacek Zienkiewicz (1997)

Studia Mathematica

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Let L be the full laplacian on the Heisenberg group n of arbitrary dimension n. Then for f L 2 ( n ) such that ( I - L ) s / 2 f L 2 ( n ) , s > 3/4, for a ϕ C c ( n ) we have ʃ n | ϕ ( x ) | s u p 0 < t 1 | e ( - 1 ) t L f ( x ) | 2 d x C ϕ f W s 2 . On the other hand, the above maximal estimate fails for s < 1/4. If Δ is the sublaplacian on the Heisenberg group n , then for every s < 1 there exists a sequence f n L 2 ( n ) and C n > 0 such that ( I - L ) s / 2 f n L 2 ( n ) and for a ϕ C c ( n ) we have ʃ n | ϕ ( x ) | s u p 0 < t 1 | e ( - 1 ) t Δ f n ( x ) | 2 d x C n f n W s 2 , l i m n C n = + .