Linear Operators: Spectral operators |
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Page 2310
... asymptotic representation of a sequence , respectively . Thus we say that a function f ( z ) defined in an unbounded set R has the asymptotic series Σx = 0 9n2 ̄ ” if N lim | 2 | ~ | ƒ ( z ) – Ž 9 , 2 ̄ " | = 0 , 00 + 121 ZER n = 0 N≥1 ...
... asymptotic representation of a sequence , respectively . Thus we say that a function f ( z ) defined in an unbounded set R has the asymptotic series Σx = 0 9n2 ̄ ” if N lim | 2 | ~ | ƒ ( z ) – Ž 9 , 2 ̄ " | = 0 , 00 + 121 ZER n = 0 N≥1 ...
Page 2325
... asymptotic representation m - ∞ En ~ 2πn + α + z2 + Σ { mn - m , m = 1 and that the zero En of M ( u ) in R ( 2 ) has the asymptotic representation ∞ En ~ 2πn + a + z2 + Σ ? m n m = 1 -m > where the Sm and 3m are certain coefficients ...
... asymptotic representation m - ∞ En ~ 2πn + α + z2 + Σ { mn - m , m = 1 and that the zero En of M ( u ) in R ( 2 ) has the asymptotic representation ∞ En ~ 2πn + a + z2 + Σ ? m n m = 1 -m > where the Sm and 3m are certain coefficients ...
Page 2340
... asymptotic expression . The coefficients a , a ' in the constant terms of A ( u ) and A ' ( μ ) are of course the same constants at a and b , of formula ( 42 ) . It now follows just as in Case 1A that the projection = E ( λm ; T ) is ...
... asymptotic expression . The coefficients a , a ' in the constant terms of A ( u ) and A ' ( μ ) are of course the same constants at a and b , of formula ( 42 ) . It now follows just as in Case 1A that the projection = E ( λm ; T ) is ...
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