Linear Operators: Spectral operators |
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Page 2011
... defined almost everywhere on S but not necessarily bounded . For every set o in Σ and every such matrix  ( s ) we ... defined operator . In general , however ,  , need not be bounded but it is always a closed and densely defined ...
... defined almost everywhere on S but not necessarily bounded . For every set o in Σ and every such matrix  ( s ) we ... defined operator . In general , however ,  , need not be bounded but it is always a closed and densely defined ...
Page 2018
... defined ( see Section VII.9 ) as the set of all complex numbers À for which ( λI — Ã ̧ ) ̄1 exists as a bounded everywhere defined operator . The spectrum σ ( A ) of A is defined to be the complement p ( A ) . It is clear from the ...
... defined ( see Section VII.9 ) as the set of all complex numbers À for which ( λI — Ã ̧ ) ̄1 exists as a bounded everywhere defined operator . The spectrum σ ( A ) of A is defined to be the complement p ( A ) . It is clear from the ...
Page 2284
... defined on the Borel sets of the plane P are positive and vanish outside en . Moreover , there is a natural continuous linear map T2 of Ex into ^ = 1 L1 ( P , B , μ1 ) with densely defined inverse . Let W2 denote the identity map of 5 ...
... defined on the Borel sets of the plane P are positive and vanish outside en . Moreover , there is a natural continuous linear map T2 of Ex into ^ = 1 L1 ( P , B , μ1 ) with densely defined inverse . Let W2 denote the identity map of 5 ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary asymptotic B₁ Banach space Boolean algebra Borel set boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complete Boolean algebra complex numbers complex plane continuous functions converges Corollary countably additive Definition denote differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem follows immediately formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality inverse L₁ Lebesgue Math multiplicity Nauk SSSR norm operators in Hilbert perturbation PROOF properties prove quasi-nilpotent resolution Russian satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose trace class type spectral operator unbounded uniformly bounded vector zero