Linear Operators, Part 2 |
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Page 2325
... formulas ( 16 ) and ( 14 ) . It also follows , from Lemma 3.5 , formula ( 16 ) , and formula ( 14 ) , that the zero En of M ( u ) in R has the asymptotic representation m m m ∞ §n ~ 2πn + a + z2 + Σ 5m n - m , m = 1 and that the zero ...
... formulas ( 16 ) and ( 14 ) . It also follows , from Lemma 3.5 , formula ( 16 ) , and formula ( 14 ) , that the zero En of M ( u ) in R has the asymptotic representation m m m ∞ §n ~ 2πn + a + z2 + Σ 5m n - m , m = 1 and that the zero ...
Page 2341
... formula ( 58 ) , that the family of all sums Ime Em J ranging over all finite sets of integers , is uniformly ... formula ( 56 ) and from formula ( 52 ) giving the form of the kernel G1 that if we excise from the angle A1 of the μ ...
... formula ( 58 ) , that the family of all sums Ime Em J ranging over all finite sets of integers , is uniformly ... formula ( 56 ) and from formula ( 52 ) giving the form of the kernel G1 that if we excise from the angle A1 of the μ ...
Page 2347
... formula ( 28 ) ( in Case 1A ) and from the corresponding formula ( 57 ) ( in Case 2 ) that - k m dk dx ( E ( λm ) f ) ( t ) is represented asymptotically by a formula of exactly the same sort , ( 28 ) or ( 57 ) , as ( E ( \ m ) f ) ( t ) ...
... formula ( 28 ) ( in Case 1A ) and from the corresponding formula ( 57 ) ( in Case 2 ) that - k m dk dx ( E ( λm ) f ) ( t ) is represented asymptotically by a formula of exactly the same sort , ( 28 ) or ( 57 ) , as ( E ( \ m ) f ) ( t ) ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
Copyright | |
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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