Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |
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Page 12
... resolvent of a similar nature . Both of these resolvents have been studied by Glenn * in his theory of the rational resol- vents of the factorable ternary forms . The general form of the ( 1 ) Sama , Dama , 0 , Þ † = am , - $ 1 , resolvent ...
... resolvent of a similar nature . Both of these resolvents have been studied by Glenn * in his theory of the rational resol- vents of the factorable ternary forms . The general form of the ( 1 ) Sama , Dama , 0 , Þ † = am , - $ 1 , resolvent ...
Page 101
... resolvent kernels , respectively . From are decreasing . Since Un ( V , 5+ In , Wn ) and we see that W and ( V , in , un ) τ n ' n are strong resolvent triplets , then by Proposition 4.2.4 ( U 6 , W ) is a strong resolvent triplet ...
... resolvent kernels , respectively . From are decreasing . Since Un ( V , 5+ In , Wn ) and we see that W and ( V , in , un ) τ n ' n are strong resolvent triplets , then by Proposition 4.2.4 ( U 6 , W ) is a strong resolvent triplet ...
Page 169
... resolvent in v * has a rational root . Again , no resolvent is valid unless it has a rational root in every resolvable case , and no quantity can serve as a resolvent unless that quantity and t are respectively rational functions of ...
... resolvent in v * has a rational root . Again , no resolvent is valid unless it has a rational root in every resolvable case , and no quantity can serve as a resolvent unless that quantity and t are respectively rational functions of ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
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 linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem 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