Linear Operators: Spectral operators |
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Page 2029
... determined by a bounded finitely additive set function v ( defined on some field of sets in RN which includes the open sets ) by the equation ( 48 ) Pn ዋ T , ( q ) = √__p ( s ) v ( ds ) , RN ΦΕΦ Similarly , functions on RN may determine ...
... determined by a bounded finitely additive set function v ( defined on some field of sets in RN which includes the open sets ) by the equation ( 48 ) Pn ዋ T , ( q ) = √__p ( s ) v ( ds ) , RN ΦΕΦ Similarly , functions on RN may determine ...
Page 2054
... determined continuous map t →→ q ( t ) of [ 0 , ∞ ) into H2 ( of ( —∞0 , 0 ] into H2 if a2 < 0 ) which is differentiable for t > 0 and has the properties ( iii ) ( iv ) ( v ) ( t ) e ( 2 ) T ( 2 ) ( RN ) , t > 0 , g ' ( t ) = Ap ( t ) ...
... determined continuous map t →→ q ( t ) of [ 0 , ∞ ) into H2 ( of ( —∞0 , 0 ] into H2 if a2 < 0 ) which is differentiable for t > 0 and has the properties ( iii ) ( iv ) ( v ) ( t ) e ( 2 ) T ( 2 ) ( RN ) , t > 0 , g ' ( t ) = Ap ( t ) ...
Page 2373
... determine discrete differential operators having eigenvalues λ = s2 determined by equations of the form .... sin s = = ks . In this case the eigenvalues are located asymptotically at the points an2 + ibn In n + the ratio of a and b ...
... determine discrete differential operators having eigenvalues λ = s2 determined by equations of the form .... sin s = = ks . In this case the eigenvalues are located asymptotically at the points an2 + ibn In n + the ratio of a and b ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary asymptotic B₁ Banach space Boolean algebra Borel set boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complete Boolean algebra complex numbers complex plane continuous functions converges Corollary countably additive Definition denote differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem follows immediately formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality inverse L₁ Lebesgue Math multiplicity Nauk SSSR norm operators in Hilbert perturbation PROOF properties prove quasi-nilpotent resolution Russian satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose trace class type spectral operator unbounded uniformly bounded vector zero