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 37
Page 2307
... formal differential operators and sets of boundary conditions lead to spectral operators . As our treatment of this example makes clear , it suffices to study differential operators of the simple form ( d / dt ) and then to use Theorem ...
... formal differential operators and sets of boundary conditions lead to spectral operators . As our treatment of this example makes clear , it suffices to study differential operators of the simple form ( d / dt ) and then to use Theorem ...
Page 2318
... function and T be the unbounded differential operator defined by a formal differential operator T = d \ 2 dx + q ( x ) and by the boundary conditions [ * ] . Then T is a spectral operator . PROOF . This follows immediately from Theorem ...
... function and T be the unbounded differential operator defined by a formal differential operator T = d \ 2 dx + q ( x ) and by the boundary conditions [ * ] . Then T is a spectral operator . PROOF . This follows immediately from Theorem ...
Page 2371
... differential equations , and by C. E. Wilder [ 1 , 2 ] , who studied the case in which linear conditions are imposed at interior points of the interval of definition of a formal differential operator . The abstract operator - theoretic ...
... differential equations , and by C. E. Wilder [ 1 , 2 ] , who studied the case in which linear conditions are imposed at interior points of the interval of definition of a formal differential operator . The abstract operator - theoretic ...
Contents
SPECTRAL OPERATORS | 1924 |
An Operational Calculus for Bounded Spectral | 1941 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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A₁ Acad adjoint operator algebra of projections Amer analytic arbitrary B-algebra B-space 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 dense differential operator Dokl Doklady Akad eigenvalues elements equation exists formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis ibid identity inequality inverse Krein L₁ Lemma locally convex spaces multiplicity Nauk SSSR norm normal operators operators in Hilbert perturbation polynomial Proc PROOF properties prove Pure Appl quasi-nilpotent resolution Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose topology trace class type spectral operator unbounded uniformly bounded vector zero