## Linear Operators: Spectral theory |

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CHAPTER XIV Linear

CHAPTER XIV Linear

**Partial**Differential Equations and Operators 1. Introduction The Cauchy Problem , Local Dependence Bu m ( 1 ) In this chapter , we shall discuss a variety of theorems having to do with linear**partial**differential ...Page 1633

A third category of formal

A third category of formal

**partial**differential operators is the parabolic , typified by the operator a 22 ox This sort of operator is closely related to the theory of semi - groups , where we have already seen general equations of the ...Page 1703

The Elliptic Boundary Value Problem Can the boundary value theory and the spectral theory of Chapter XIII be generalized to

The Elliptic Boundary Value Problem Can the boundary value theory and the spectral theory of Chapter XIII be generalized to

**partial**differential operators ? In the present section it will be seen that it can , at least for the class of ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Miscellaneous Applications | 937 |

Compact Groups | 945 |

Copyright | |

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additive adjoint operator 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 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