## Linear Operators: Spectral theory |

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Page 1420

If A is considered as a subset of H , then the restriction of T2 ( t ' ) to A is a

continuous mapping of A into H . Then , assuming that itt has a non -

coefficient , ( A ) the Hilbert spaces D ( T2 ( t + r ' ) ) and D ( T1 ( ) ) have the same

...

If A is considered as a subset of H , then the restriction of T2 ( t ' ) to A is a

continuous mapping of A into H . Then , assuming that itt has a non -

**zero**leadingcoefficient , ( A ) the Hilbert spaces D ( T2 ( t + r ' ) ) and D ( T1 ( ) ) have the same

...

Page 1432

... Be is analytic in the neighborhood of

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

singularity at all , and

... Be is analytic in the neighborhood of

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

**zero**. If v = 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

tita - fatı identically

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

tita - fatı identically

**zero**in [ c , d ] . Thus ( hta ? ) ' = tz " ( ita - tata ) is identically**zero**in [ c , d ] , so that fit is constant . Moreover , since fı and fí have only a finite ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 869 |

Commutative BAlgebras | 877 |

Copyright | |

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additive adjoint adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure coefficients commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension fact finite follows formal differential operator formula function function f give given Hence Hilbert space ideal identity independent indices inequality integral interval isometric isomorphism Lemma linear mapping matrix measure multiplicity neighborhood norm normal operator obtained positive preceding present projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique unit vanishes vector zero