## Linear Operators: Spectral theory |

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Page 1191

However , this operator is not self

However , this operator is not self

**adjoint**for it is clear from the above equations that any function g with a continuous first derivative has the property that d ( i np to 8 ) = ( 1,1 mm ) . d , g dt d 8 dt jed ( ) . dt and thus any ...Page 1239

1 = Conversely , let T , be a self

1 = Conversely , let T , be a self

**adjoint**extension of T. Then by Lemma 26 , T , is the restriction of T * to a subspace W of D ( T * ) determined by a symmetric family of linearly independent boundary conditions B ( x ) = 0 , i = 1 ...Page 1290

that since ti = ( 12tı ) * , the operator n Σ ( -1 ) : -1 ) " ( ( ) P. Pilt ) ( 1 ) dt dt same n n is formally self

that since ti = ( 12tı ) * , the operator n Σ ( -1 ) : -1 ) " ( ( ) P. Pilt ) ( 1 ) dt dt same n n is formally self

**adjoint**provided only that the coefficients Pi are real . In the way , the formal differential operator ( 1/2 ) ( d / dt ) ...### 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