Linear Operators, Part 2 |
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Page 1902
... section is dependent on any section to which it is connected by a rising line , except that ( b ) a section dependent on a dotted section , or on a section in Volume I or Volume II ( Chapters I - XIV ) , is dependent on every section on ...
... section is dependent on any section to which it is connected by a rising line , except that ( b ) a section dependent on a dotted section , or on a section in Volume I or Volume II ( Chapters I - XIV ) , is dependent on every section on ...
Page 2291
... Section 3 is greatly generalized in Section 4 , we feel that it is worth inserting the simpler case of Section 3 as a kind of preparation for the more complicated case . The question of deciding when the generalized eigenfunctions of an ...
... Section 3 is greatly generalized in Section 4 , we feel that it is worth inserting the simpler case of Section 3 as a kind of preparation for the more complicated case . The question of deciding when the generalized eigenfunctions of an ...
Page 2376
... section we shall show that this program can be carried through successfully if q is of a degree of small- ness ... Section 1 ? For what a , b , c is this operator spectral ? In Section 2 we study an interesting idea due to Friedrichs ...
... section we shall show that this program can be carried through successfully if q is of a degree of small- ness ... Section 1 ? For what a , b , c is this operator spectral ? In Section 2 we study an interesting idea due to Friedrichs ...
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