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

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Page 1298

First of all , it is

First of all , it is

**clear**from the preceding definition that the set M. ( the set M , ) of boundary values at a ( at b ) is a subspace of the space M of all boundary values . Let fi and fa be two functions in C® ( 1 ) such that fı ( t ) ...Page 1373

**Clearly**, if V is as in Theorem 13 ( i ) , û = AV . It is**clear**from the definition of A that for each n - tuple F [ 1 , ... , In ] of Borel functions defined on 1 , AF € L2 ( 1 , { ôi ; } ) if and only if FeL2 ( 4 , { p } ) .Page 1689

Indeed , if { Am } is a Cauchy sequence in L ( 1 ) , it is

Indeed , if { Am } is a Cauchy sequence in L ( 1 ) , it is

**clear**from ( i ) that { 2+ { m } is a Cauchy sequence in L ( I ) for IJ Sk , so that there exist functions g , gol in L , ( I ) such that limm - com - glp = 0 and limm - c1011m ...### 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 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 uniformly unique unit unitary vanishes vector zero