## Linear Operators: Spectral theory |

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Page 1260

17 ( Schmidt ) The non -

eigenvalues of TT * , even as to multiplicity ( the positive square roots of these

eigenvalues are sometimes called the characteristic numbers of T ) . 18 Let T be

a ...

17 ( Schmidt ) The non -

**zero**eigenvalues of T * T are the same as the non -**zero**eigenvalues of TT * , even as to multiplicity ( the positive square roots of these

eigenvalues are sometimes called the characteristic numbers of T ) . 18 Let T be

a ...

Page 1432

... Bx is analytic in the neighborhood of

is called the order of the singularity of equation [ * ] at

singularity at all , and

... Bx is analytic in the neighborhood of

**zero**for 0 < k En and u < v . In this case , vis called the order of the singularity of equation [ * ] at

**zero**. If y = 0 , there is nosingularity at all , and

**zero**is called a regular point of the differential equation .Page 1463

Since all the terms in the integral on the right are non - negative , we must have

t1fa - fatı identically

only a finite number of

( t ) ...

Since all the terms in the integral on the right are non - negative , we must have

t1fa - fatı identically

**zero**in [ c , d ] . Thus ( total ) ... Moreover , since fı and tí haveonly a finite number of

**zeros**in [ c , d ] , we must have pi ( t ) = pz ( t ) , q . ( t ) = 92( t ) ...

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### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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additive Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complete Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense derivatives determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure Nauk neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero