Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 54
Page 1051
... evident from Definition 1. Statements ( ii ) and ( iii ) are evident consequences of Definition 1 and of the formulae √ gn P ( x ) dx = √ g „ ¥ ( Ux ) dxæ , En En -n √gn 4 ( xx ) dx = | x | ̄ ” √gn P ( x ) dx , En En which are valid ...
... evident from Definition 1. Statements ( ii ) and ( iii ) are evident consequences of Definition 1 and of the formulae √ gn P ( x ) dx = √ g „ ¥ ( Ux ) dxæ , En En -n √gn 4 ( xx ) dx = | x | ̄ ” √gn P ( x ) dx , En En which are valid ...
Page 1347
... evident advantage that it makes o , ( , 2 ) an entire function of the complex variable 2 ; but it has drawbacks which , though less evident , are nevertheless decisive . Suppose , for example , that we study the self adjoint operator T ...
... evident advantage that it makes o , ( , 2 ) an entire function of the complex variable 2 ; but it has drawbacks which , though less evident , are nevertheless decisive . Suppose , for example , that we study the self adjoint operator T ...
Page 1756
... evident consequence of 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 ...
... evident consequence of 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 ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
57 other sections not shown
Other editions - View all
Common terms and phrases
adjoint extension adjoint operator algebra analytic B-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers 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 Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma PROOF prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology tr(T transform unique unitary vanishes vector zero