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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Results 1-3 of 9
Page 2320
... boundary values for 7. Thus , by Corollary XIII.2.23 , there exist two nxn matrices ( 1 ) n - 1 α ;; and B , such ... boundary conditions at the outset . Suppose that if B is a boundary value , we agree to call the order of the highest ...
... boundary values for 7. Thus , by Corollary XIII.2.23 , there exist two nxn matrices ( 1 ) n - 1 α ;; and B , such ... boundary conditions at the outset . Suppose that if B is a boundary value , we agree to call the order of the highest ...
Page 2343
... boundary values ( 1 ) may be separated into a set of v boundary values at zero and a set of v boundary values at 1 . We state all this as a formal theorem . 14 THEOREM ( H. P. Kramer ) . Let n be even and let T be the closed operator ...
... boundary values ( 1 ) may be separated into a set of v boundary values at zero and a set of v boundary values at 1 . We state all this as a formal theorem . 14 THEOREM ( H. P. Kramer ) . Let n be even and let T be the closed operator ...
Page 2491
... boundary values at a and no boundary values at b . A common boundary condition A ( ƒ ) = 0 for all the operators 7 is imposed ; in this way , a family T , of self adjoint operators is defined . It is then established that ( 1 ) under ...
... boundary values at a and no boundary values at b . A common boundary condition A ( ƒ ) = 0 for all the operators 7 is imposed ; in this way , a family T , of self adjoint operators is defined . It is then established that ( 1 ) under ...
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