Linear Operators, Part 2 |
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Page 2331
... uniformly bounded for μ in Co and m ≥ 1 ( by formula ( 4 ) ) and that ox ( 1 − y , μ + 2πm ) = σ¿ ( 1 — y , μ ) σ „ ( 1 — у , 2πm ) ( by this same formula ) , to establish the following two separate assertions . - --- ( a ) For 0 ≤ k ...
... uniformly bounded for μ in Co and m ≥ 1 ( by formula ( 4 ) ) and that ox ( 1 − y , μ + 2πm ) = σ¿ ( 1 — y , μ ) σ „ ( 1 — у , 2πm ) ( by this same formula ) , to establish the following two separate assertions . - --- ( a ) For 0 ≤ k ...
Page 2347
... uniform boundedness theorem , Corollary II.3.21 ) that for each ƒ in L2 , the set of functions ( v ) - k d k £ m2 ( 4 ) PK , m = K dx ( E ( \ m ) ƒ ) ( t ) , is uniformly bounded in L2 ( 0 , 1 ) . It follows from formula ( 28 ) ( in ...
... uniform boundedness theorem , Corollary II.3.21 ) that for each ƒ in L2 , the set of functions ( v ) - k d k £ m2 ( 4 ) PK , m = K dx ( E ( \ m ) ƒ ) ( t ) , is uniformly bounded in L2 ( 0 , 1 ) . It follows from formula ( 28 ) ( in ...
Page 2361
... bounded domains covering the whole complex plane , and suppose that minze u z❘ = ∞o . Let V , be the boundary of ... uniformly bounded for each ƒe S. ( ( T + P ) * ) . However , in the course of the proof of Theorem 6 it was ...
... bounded domains covering the whole complex plane , and suppose that minze u z❘ = ∞o . Let V , be the boundary of ... uniformly bounded for each ƒe S. ( ( T + P ) * ) . However , in the course of the proof of Theorem 6 it was ...
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