Linear Operators, Part 2 |
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Page 1909
... present a number of important applica- tions of the general theory of spectral operators , whose discussion re ... present the abstract operator theory in the text , and then in the Notes and Remarks , especially in Section XX.6 , give ...
... present a number of important applica- tions of the general theory of spectral operators , whose discussion re ... present the abstract operator theory in the text , and then in the Notes and Remarks , especially in Section XX.6 , give ...
Page 2058
... present state of the universe , tell with absolute certainty its exact state at any time , future or past . The obvious impossibility of the existence of an intelligence so superior that it could ascertain the initial conditions ( the ...
... present state of the universe , tell with absolute certainty its exact state at any time , future or past . The obvious impossibility of the existence of an intelligence so superior that it could ascertain the initial conditions ( the ...
Page 2227
... present chapter is an attempt to make the corresponding step in the theory of spectral operators . We begin by defining a closed spectral operator and its resolution of the identity , and showing that the latter is unique . Then a ...
... present chapter is an attempt to make the corresponding step in the theory of spectral operators . We begin by defining a closed spectral operator and its resolution of the identity , and showing that the latter is unique . Then a ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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 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