Linear Operators: Spectral operators |
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Page 2017
... inequality ( i ) of Theorem 6 holds . Here the set S1 is void so that A is a scalar type spectral operator to which Theorem 5 applies . Another type of differential operator whose extension is a spectral operator which is not a scalar ...
... inequality ( i ) of Theorem 6 holds . Here the set S1 is void so that A is a scalar type spectral operator to which Theorem 5 applies . Another type of differential operator whose extension is a spectral operator which is not a scalar ...
Page 2190
... inequality of the theorem . From this inequality it is evident that the homomorphism ƒ → S ( ƒ ) is an isomorphism and that the algebra { S ( ƒ ) | ƒ € EB ( A , S ) } is a B - algebra . To complete the proof of the theorem it only ...
... inequality of the theorem . From this inequality it is evident that the homomorphism ƒ → S ( ƒ ) is an isomorphism and that the algebra { S ( ƒ ) | ƒ € EB ( A , S ) } is a B - algebra . To complete the proof of the theorem it only ...
Page 2403
... inequality for integral operators ( Lemma 5 below ) which is elementary in the sense that it relates only to the norms of the integral kernels involved . We then use this inequality to apply Theorem 1 in an illustrative but somewhat ...
... inequality for integral operators ( Lemma 5 below ) which is elementary in the sense that it relates only to the norms of the integral kernels involved . We then use this inequality to apply Theorem 1 in an illustrative but somewhat ...
Contents
SPECTRAL OPERATORS | 1924 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
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 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