## Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |

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Page 1051

Statement ( i ) is

Statement ( i ) is

**evident**from Definition 1. Statements ( ii ) and ( iii ) are**evident**consequences of Definition 1 and of the formulae En Sen g ( x ) dx = Sen ( Ux ) dx , 9 Sen clax ) dx = 121 - SemP ( ) dx , " which are valid for ...Page 1173

The space L , ( L , ) may in an

The space L , ( L , ) may in an

**evident**manner be identified with the L , -space on the product set E " XS and the inequality to be proved reduces to ( 11 ) SAS $ 2 ( x - Y ) fly , s ) dy dvds ( en lx y " SC SS 1 / ( 2,6 ) | P dads .Page 1347

This procedure has the

This procedure has the

**evident**advantage that it makes 0 ; ( :, 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 ...### What people are saying - Write a review

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additive adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined eigenvalues element equal equation Exercise exists extension fact finite dimensional follows formal formal differential operator formula function function f given Hence Hilbert space Hilbert-Schmidt ideal identity independent inequality integral interval isometric isomorphism Lemma limit linear Ly(R matrix measure multiplicity neighborhood norm normal operator obtained orthonormal positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown shows solution spectral spectrum square-integrable statement subset subspace sufficient Suppose symmetric Theorem theory topology transform unique unit unitary vanishes vector zero