Linear Operators: Spectral operators |
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Page 2021
... equation Aq = 0 , being equivalent to the Cauchy - Riemann equation for the real and imaginary parts of a holomorphic function , has no non - zero solution in 2 . For , by classical function theory , any solution = ( 1 , 2 ) in Ø2 of ...
... equation Aq = 0 , being equivalent to the Cauchy - Riemann equation for the real and imaginary parts of a holomorphic function , has no non - zero solution in 2 . For , by classical function theory , any solution = ( 1 , 2 ) in Ø2 of ...
Page 2073
... equation in ( 27 ) follows from the definitions of the operators ( f ) , the second from the fact that they belong to the commutative algebra A1 , and equation ( 28 ) follows from ( 26 ) . + With each operator a in A1 we associate an ...
... equation in ( 27 ) follows from the definitions of the operators ( f ) , the second from the fact that they belong to the commutative algebra A1 , and equation ( 28 ) follows from ( 26 ) . + With each operator a in A1 we associate an ...
Page 2074
... equation ( 36 ) . Then ( 31 ) shows that x is in H. and equation ( 35 ) holds . This means that for some vector z in H. we have + et ( 9- ) y = e − 3 e − 5 ( 0 + ) x + % , and , using ( 30 ) , it is seen that - y = ax + e - 3 ( 9 ...
... equation ( 36 ) . Then ( 31 ) shows that x is in H. and equation ( 35 ) holds . This means that for some vector z in H. we have + et ( 9- ) y = e − 3 e − 5 ( 0 + ) x + % , and , using ( 30 ) , it is seen that - y = ax + e - 3 ( 9 ...
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