Wyniki wyszukiwania

1

Commutativity of compact selfadjoint operators

100%

Greiner G., Ricker W. J.

Studia Mathematica

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1994-1995

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tom 112

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nr 2

109-125

EN

The relationship between the joint spectrum γ(A) of an n-tuple $A = (A_1,..., A_n)$ of selfadjoint operators and the support of the corresponding Weyl calculus T(A) : f ↦ f(A) is discussed. It is shown that one always has γ(A) ⊂ supp (T(A)). Moreover, when the operators are compact, equality occurs if and only if the operators $A_j$ mutually commute. In the non-commuting case the equality fails badly: While γ(A) is countable, supp(T(A)) has to be an uncountable set. An example is given showing that, for non-compact operators, coincidence of γ(A) and supp (T(A)) no longer implies commutativity of the set ${A_i}$ .

2

On p-dependent local spectral properties of certain linear differential operators in $L^{p}(ℝ^{N})

100%

Albrecht E., Ricker W. J.

Studia Mathematica

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1998

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tom 130

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nr 1

23-52

EN

The aim is to investigate certain spectral properties, such as decomposability, the spectral mapping property and the Lyubich-Matsaev property, for linear differential operators with constant coefficients ( and more general Fourier multiplier operators) acting in $L^p(ℝ^N)$. The criteria developed for such operators are quite general and p-dependent, i.e. they hold for a range of p in an interval about 2 (which is typically not (1,∞)). The main idea is to construct appropriate functional calculi: this is achieved via a combination of methods from the theory of Fourier multipliers and local spectral theory.

3

Continuous extensions of spectral measures

100%

Okada S., Ricker W. J.

Colloquium Mathematicum

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1996

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tom 71

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nr 1

115-132

4

Compactness properties of vector-valued integration maps in locally convex spaces

100%

Okada S., Ricker W. J.

Colloquium Mathematicum

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1994

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tom 67

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nr 1

1-14

Ograniczanie wyników

2 Colloquium Mathematicum

2 Studia Mathematica

4 Ricker W. J.

2 Okada S.

1 Albrecht E.

1 Greiner G.

1 1998

1 1996

1 1995

1 1994

Commutativity of compact selfadjoint operators

On p-dependent local spectral properties of certain linear differential operators in $L^{p}(ℝ^{N})

Continuous extensions of spectral measures

Compactness properties of vector-valued integration maps in locally convex spaces