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

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Page 1527

The same process applied to the hypergeometric

The same process applied to the hypergeometric

**equation**[ 1 ] shows that ( x , y ; z ) satisfies the confluent ... To deal with the confluent hypergeometric**equation**we must consequently use some of the theory of**equations**with ...Page 1528

The first of these algebraic

The first of these algebraic

**equations**, which is simply the characteristic**equation**of the differential**equation**, is quadratic ; all the ... If we find the differential**equation**L'f ' = 0 satisfied by f ' = { exp ( 5 ( 1 ) zk - 1 + .Page 1529

The confluent hypergeometric

The confluent hypergeometric

**equation**has the characteristic**equation**a ? - = 0 , so that 511 ) = 0,5 - 0,5 ) = 1. Thus the Stokes lines for this**equation**are the positive and negative imaginary axes . Trying solutions of the form z ...### 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