Linear Operators, Part 2 |
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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 ...
... 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 ...
Page 2318
... function and T be the unbounded differential operator defined by a formal differential operator ¬ = - d2 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 ¬ = - d2 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 |
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