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

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If to

If to

**exists**in B ( X ) , then T.-T. = ) Tx [ ( Ta'y ) x ] = yz , ( To'y ) z = T ; ' ( yz ) , and if a = Tile ... An element æ in a B - algebra X is said to be regular in case x - 1**exists**in X. It is singular if it is not regular .Page 1057

By Lemma 2 , the integral 0 ( tu )

By Lemma 2 , the integral 0 ( tu )

**exists**if 0 ( u )**exists**and t > 0 ; and the integral 0 ( Vu )**exists**and equals PS S. 14 ) en 1x ! En 12 ( x ) 2 ( Vy ) ei ( x , Vu ) dx eily , u ) dy \ y \ " if Plen2 ( Vy ) \ y - n pilv , u ) dy ...Page 1261

23 If an operator T has a closed linear extension there

23 If an operator T has a closed linear extension there

**exists**a unique closed linear extension T such that if T , is any closed linear , extension of T then I CT , T is called the closure of T. ( a ) There**exists**a densely defined ...### 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