## Linear Operators: Spectral theory |

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Page 1080

I 34 ( Bendixon ) Let A be as in Exercise 25 , and suppose also that the matrix

I 34 ( Bendixon ) Let A be as in Exercise 25 , and suppose also that the matrix

**elements**of A are real . Let C = ( A - A * ) , and let g be the maximum of the absolute values of the matrix**elements**of C. Then H. -1 ) ) Ill 5g ( 2 ( Hint ...Page 1339

An

An

**element**F of Ly ( { Mi ; } ) will be said to be a { M ij } -null function if | F1 = 0. The set of all equivalence classes of**elements**of Ly ( { uis } ) modulo { uij } -null functions will be denoted by L2 ( { i ; } ) .Page 1436

Let { en } be a bounded sequence of

Let { en } be a bounded sequence of

**elements**of D ( T ) such that { Ter } converges . Find a subsequence { gn , } = { h ; } such that x * ( h ; ) converges for each 1 , 1 sisk . Then ħ ; = h ; - * __ ** ( h ; ) 9 ; is in D , and Thi Thi ...### 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