Linear Operators: Spectral operators |
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Page 1909
... theory forms an excellent introduction to the detailed study of the much more refined and complete theory of self adjoint operators in Hilbert space . It soon became evident , however , that the natural limitations imposed by size ...
... theory forms an excellent introduction to the detailed study of the much more refined and complete theory of self adjoint operators in Hilbert space . It soon became evident , however , that the natural limitations imposed by size ...
Page 2112
... theory of type 3 if for arbitrary open sets G1 , ... , Gn which cover the complex plane , there exist closed linear subspaces M1 , ... , M , which span X , are invariant under T , and such that o ( T | M1 ) ≤ G1 , i = 1 , ... , n ...
... theory of type 3 if for arbitrary open sets G1 , ... , Gn which cover the complex plane , there exist closed linear subspaces M1 , ... , M , which span X , are invariant under T , and such that o ( T | M1 ) ≤ G1 , i = 1 , ... , n ...
Page 2227
... theory of Hermitian operators to ordinary and partial differential operators it is first necessary to extend the spectral theory of bounded operators to a theory of unbounded operators . The present chapter is an attempt to make the ...
... theory of Hermitian operators to ordinary and partial differential operators it is first necessary to extend the spectral theory of bounded operators to a theory of unbounded operators . The present chapter is an attempt to make the ...
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