Linear Operators, Part 2 |
From inside the book
Results 1-3 of 84
Page 1021
... statement to be established may be written as | det ( B ) ( B − 18 „ , ≈ ) | ≤ | x | || B || n − 1 ( n − 1 ) − ( n − 1 ) / 2 ̧ By expressing this statement in terms of determinants , it is seen that it suffices to prove the lemma ...
... statement to be established may be written as | det ( B ) ( B − 18 „ , ≈ ) | ≤ | x | || B || n − 1 ( n − 1 ) − ( n − 1 ) / 2 ̧ By expressing this statement in terms of determinants , it is seen that it suffices to prove the lemma ...
Page 1653
... Statement ( i ) follows from statement ( ii ) by Definitions 15 ( iii ) and 17 ( ii ) . Statement ( iii ) follows from statement ( ii ) and the fact that F ( +1 ) F ( x ) for all k ≥0 and F in H ( +1 ) ( I ) , ( cf. Definition 15 ( i ) ...
... Statement ( i ) follows from statement ( ii ) by Definitions 15 ( iii ) and 17 ( ii ) . Statement ( iii ) follows from statement ( ii ) and the fact that F ( +1 ) F ( x ) for all k ≥0 and F in H ( +1 ) ( I ) , ( cf. Definition 15 ( i ) ...
Page 1756
... statement ( i ) . Moreover , statement ( i ) enables us to reduce the proof of the existence of the function V to the proof of the following statement . ( ii ) For each r > 0 and p ≥ 1 , there exists a function V in ĈP ( E " ) , such ...
... statement ( i ) . Moreover , statement ( i ) enables us to reduce the proof of the existence of the function V to the proof of the following statement . ( ii ) For each r > 0 and p ≥ 1 , there exists a function V in ĈP ( E " ) , such ...
Contents
BAlgebras | 861 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
56 other sections not shown
Other editions - View all
Common terms and phrases
adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers constant continuous function converges Corollary deficiency indices Definition denote dense eigenvalues element equation essential spectrum Exercise exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology unique unitary vanishes vector zero