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 1905
... Equations By F. G. Tricomi Differential Equations : Geometric Theory By Solomon Lefshetz Linear Operators - Parts I , II , and III By Nelson Dunford and Jacob T. Schwartz Modern Geometrical Optics By Max Herzberger Orthogonal Functions ...
... Equations By F. G. Tricomi Differential Equations : Geometric Theory By Solomon Lefshetz Linear Operators - Parts I , II , and III By Nelson Dunford and Jacob T. Schwartz Modern Geometrical Optics By Max Herzberger Orthogonal Functions ...
Page 2049
... differential equations , the Cauchy problem ( 103 ) for it reduces the problem to that of a quadrature . We shall first illustrate the use of ( 104 ) by solving the diffusion equation with p = 1 , N arbitrary , and the initial value a ...
... differential equations , the Cauchy problem ( 103 ) for it reduces the problem to that of a quadrature . We shall first illustrate the use of ( 104 ) by solving the diffusion equation with p = 1 , N arbitrary , and the initial value a ...
Page 2373
... differential operators having eigenvalues λ = s2 determined by equations of the form sin s = - ks . In this case the ... differential equations . THEOREM . Let T be an unbounded discrete self adjoint XIX.6 2373 NOTES AND REMARKS Notes ...
... differential operators having eigenvalues λ = s2 determined by equations of the form sin s = - ks . In this case the ... differential equations . THEOREM . Let T be an unbounded discrete self adjoint XIX.6 2373 NOTES AND REMARKS Notes ...
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