## Linear Operators: Spectral theory |

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Page 1348

In the range a > 0 they form a perfectly suitable basis for the

In the range a > 0 they form a perfectly suitable basis for the

**solutions**of to ho . However , in the range 2 < 0,14 is imaginary , and an analytic expression like cos att is hard to work with because of the apparent ambiguity in the ...Page 1392

In this case , however , the problem of choosing a basis for the

In this case , however , the problem of choosing a basis for the

**solutions**of to = ho is by no means trivial . If , for instance , we take r = - ( d / dt ) 2 + t2 , then the**solutions**of to = lo are particular confluent hypergeometric ...Page 1632

and imaginary parts of a

and imaginary parts of a

**solution**of the equation V2f = 0 in the region R = { { x1 , x2 ] \ x2 > 0 } are the real ... be able to construct**solutions**of the equation v2f O which vanish in a domain of R but are not identically zero .### What people are saying - Write a review

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### Contents

8 | 876 |

859 | 885 |

extensive presentation of applications of the spectral theorem | 911 |

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additive adjoint adjoint operator algebra analytic assume 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 domain eigenvalues elements equal equation equivalent Exercise exists extension fact finite dimensional follows follows from Lemma formal differential operator formula function given Hence Hilbert space Hilbert-Schmidt ideal identity immediately implies independent inequality integral interval invariant isometric isomorphism Lemma limit linear Ly(R mapping matrix measure multiplicity neighborhood norm obtained orthonormal positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown shows solutions spectral spectrum square-integrable statement subset subspace sufficient Suppose symmetric Theorem theory topology transform uniformly unique unit unitary vanishes vector zero