Linear Operators: Spectral operators |
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Page 2029
... determined by a bounded finitely additive set function v ( defined on some field of sets in RN which includes the open sets ) by the equation ( 48 ) T , ( q ) = √__p ( s ) v ( ds ) , RN φεΦ . Similarly , functions on RN may determine ...
... determined by a bounded finitely additive set function v ( defined on some field of sets in RN which includes the open sets ) by the equation ( 48 ) T , ( q ) = √__p ( s ) v ( ds ) , RN φεΦ . Similarly , functions on RN may determine ...
Page 2184
... determined spectral measure . This is the analogue of the general spectral theorem for algebras of normal operators in Hilbert space ( cf. X.2.1 ) . 4 THEOREM . Let A be an algebra of operators in the complex B - space X which is the ...
... determined spectral measure . This is the analogue of the general spectral theorem for algebras of normal operators in Hilbert space ( cf. X.2.1 ) . 4 THEOREM . Let A be an algebra of operators in the complex B - space X which is the ...
Page 2316
... determined so as to satisfy It follows readily that - 1g , ko lớn 1 sin Bn = cos Bn . ᅲ so that Br = 2 Pn ( t ) = cos ( 8 , t + Sn ) , It follows that ( nako ) -1 + 0 ( n - 2 ) , - 1 Sn = ( nπk 。) ̄1 + O ( n − 2 ) . S * ( 92 ( t ) ...
... determined so as to satisfy It follows readily that - 1g , ko lớn 1 sin Bn = cos Bn . ᅲ so that Br = 2 Pn ( t ) = cos ( 8 , t + Sn ) , It follows that ( nako ) -1 + 0 ( n - 2 ) , - 1 Sn = ( nπk 。) ̄1 + O ( n − 2 ) . S * ( 92 ( t ) ...
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