Linear Operators: Spectral operators |
From inside the book
Results 1-3 of 89
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 Ф in 2. For , by classical function theory , any solution = ( 1 , 2 ) in 2 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 Ф in 2. For , by classical function theory , any solution = ( 1 , 2 ) in 2 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 es ( 9- ) y = e − 3e - ? ( 9+ ) x + % , and , using ( 30 ) , it is seen that y = ax + e - 5 ( 9 − ) z . + ...
... 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 es ( 9- ) y = e − 3e - ? ( 9+ ) x + % , and , using ( 30 ) , it is seen that y = ax + e - 5 ( 9 − ) z . + ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
20 other sections not shown
Other editions - View all
Common terms and phrases
A₁ adjoint operator algebra of projections Amer analytic arbitrary asymptotic B₁ Banach space Boolean algebra Borel set boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complete Boolean algebra complex numbers complex plane continuous functions converges Corollary countably additive Definition denote differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem follows immediately formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality inverse L₁ Lebesgue Math multiplicity Nauk SSSR norm operators in Hilbert perturbation PROOF properties prove quasi-nilpotent resolution Russian satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose trace class type spectral operator unbounded uniformly bounded vector zero