Linear Operators, Part 2 |
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Page 2056
... assumed that man's fate was determined by himself but not by an act of free will . Plato ( 427-347 B.C. ) and Socrates ( 469–399 ? B.C. ) assumed that one's decisions were made for one's own good and thus in any situation a man's ...
... assumed that man's fate was determined by himself but not by an act of free will . Plato ( 427-347 B.C. ) and Socrates ( 469–399 ? B.C. ) assumed that one's decisions were made for one's own good and thus in any situation a man's ...
Page 2151
... assumed that there is a function § = έ ( t , 8 ) which is twice continuously differentiable on its domain −1 ≤t , d ≤ 1 of definition and which has the following properties . The equation ( −1 , 8 ) = ( +1,8 ) holds for all 8 in the ...
... assumed that there is a function § = έ ( t , 8 ) which is twice continuously differentiable on its domain −1 ≤t , d ≤ 1 of definition and which has the following properties . The equation ( −1 , 8 ) = ( +1,8 ) holds for all 8 in the ...
Page 2497
... Assumption A may be stated , roughly and heuristically , as the assump- tion that no point eigenvalue of T + K lies in ... assumed to be real , so that the wave operator method is available . For improvements of this sort , together with ...
... Assumption A may be stated , roughly and heuristically , as the assump- tion that no point eigenvalue of T + K lies in ... assumed to be real , so that the wave operator method is available . For improvements of this sort , together with ...
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