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

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Page 1310

Then the boundary conditions are real , and there is exactly one

Then the boundary conditions are real , and there is exactly one

**solution**( t , 2 ) of ( 1-2 ) = 0 square - integrable at a and satisfying the q 9 boundary conditions at a , and exactly one**solution**y ( t , 2 ) of ( 1-2 ) y = 0 square ...Page 1529

Then in this angle any

Then in this angle any

**solution**of Lf = 0 whose asymptotic expansion begins with the factor exp ( 511 ) 2k - 1 ) is exponentially small ( as [ 3 ] → o in the angle ) relative to any**solution**whose asymptotic expansion begins with the ...Page 1554

has a

has a

**solution**with a finite number of zeros and has a squareintegrable**solution**. Prove that the equation g ' ' ( t ) -92 ( t ) g ( t ) = 0 1 . has a square - integrable**solution**. ( Hint : Write g ( t ) = h ( t ) / ( t ) and obtain ...### 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