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 algebra Amer analytic applications arbitrary B-space Banach Banach space Boolean algebra Borel sets boundary bounded Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding defined Definition denote dense determined differential operator Doklady Akad elements equation equivalent established example exists extension finite follows formula function given gives H₁ Hence Hilbert space hypothesis identity integral invariant inverse Lemma limit linear operators Math multiplicity Nauk SSSR norm normal perturbation plane positive preceding present problem Proc projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero