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 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
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Common terms and phrases
A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded Borel function bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain eigenvalues elements equation exists finite number follows from Lemma follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial PROOF properties prove quasi-nilpotent resolution Russian S₁ satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset subspace Suppose trace class type spectral operator unbounded uniformly bounded unique vector zero