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 2 of the ...
... 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 2 of the ...
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 ( o - by = e - Be - ( ( @ + ) x + % , y = ax + e - 5 ( 9- ) z . and , using ( 30 ) , it is seen that ...
... 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 ( o - by = e - Be - ( ( @ + ) x + % , y = ax + e - 5 ( 9- ) z . and , using ( 30 ) , it is seen that ...
Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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Common terms and phrases
A₁ adjoint operator algebra of projections Amer arbitrary B*-algebra B₁ Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator Colojoară commuting compact complex numbers complex plane contains converges Corollary countably additive Definition dense differential operator disjoint Doklady Akad E-measurable eigenvalues elements equation equivalent exists Foias follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math matrix multiplicity norm operators in Hilbert perturbation polynomial PROOF proved quasi-nilpotent resolution restriction Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset subspace sufficiently type spectral operator unbounded unique vector weakly complete zero