## Linear Operators: Self Adjoint Operators in Hilbert Space. Spectral theory. Part II |

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Page 1503

Examples We now wish to illustrate the application of the preceding theory to

specific

past few sections , he will find it evident that in applying the general methods to ...

Examples We now wish to illustrate the application of the preceding theory to

specific

**differential equations**. If the reader surveys the theory developed in thepast few sections , he will find it evident that in applying the general methods to ...

Page 1528

Sk - 1 ) , ez ] , i = 1 , 2 , are called the characteristic sets for the irregular

singularity at infinity of the

coefficients .

Sk - 1 ) , ez ] , i = 1 , 2 , are called the characteristic sets for the irregular

singularity at infinity of the

**differential equation**. ... series into the**differential****equation**, and solving the resulting sequence of algebraic equations for thecoefficients .

Page 1629

CHAPTER XIV Linear Partial

The Cauchy Problem , Local Dependence m In this chapter , we shall discuss a

variety of theorems having to do with linear partial differential operators .

CHAPTER XIV Linear Partial

**Differential Equations**and Operators 1. IntroductionThe Cauchy Problem , Local Dependence m In this chapter , we shall discuss a

variety of theorems having to do with linear partial differential operators .

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Preliminary Notions | 865 |

Copyright | |

61 other sections not shown

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### Common terms and phrases

additive Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity 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