Linear Operators: Spectral operators |
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Page 2010
... Unbounded Spectral Operators Although the topic of unbounded spectral operators will be treated in some detail in Chapter XVIII and many illustrations of such operators will be found in Chapters XIX and XX , we introduce the subject ...
... Unbounded Spectral Operators Although the topic of unbounded spectral operators will be treated in some detail in Chapter XVIII and many illustrations of such operators will be found in Chapters XIX and XX , we introduce the subject ...
Page 2013
... unbounded convolution . The preceding discussion may be summarized as follows . 2 THEOREM . For each measurable p xp matrix A ( s ) of complex functions defined almost everywhere on S and each measurable set o in S the operators  , and ...
... unbounded convolution . The preceding discussion may be summarized as follows . 2 THEOREM . For each measurable p xp matrix A ( s ) of complex functions defined almost everywhere on S and each measurable set o in S the operators  , and ...
Page 2227
... unbounded operators . The present chapter is an attempt to make the corresponding step in the theory of spectral operators . We ... Unbounded Spectral Operators 1 DEFINITION . Let B denote 2227 Unbounded Spectral Operators 1 Introduction.
... unbounded operators . The present chapter is an attempt to make the corresponding step in the theory of spectral operators . We ... Unbounded Spectral Operators 1 DEFINITION . Let B denote 2227 Unbounded Spectral Operators 1 Introduction.
Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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Common terms and phrases
A₁ adjoint operator algebra of projections Amer arbitrary B*-algebra B₁ Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator Colojoară commuting compact complex numbers complex plane contains converges Corollary countably additive Definition dense differential operator disjoint Doklady Akad E-measurable eigenvalues elements equation equivalent exists Foias follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math matrix multiplicity norm operators in Hilbert perturbation polynomial PROOF proved quasi-nilpotent resolution restriction Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset subspace sufficiently type spectral operator unbounded unique vector weakly complete zero