## Linear Operators: Spectral theory |

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Page 1629

Problem, Local Dependence In this chapter, ... Since the theory of linear

differential operators is vast and highly ramified, we shall only touch upon a

number of ...

**Partial**. Differential. Equations. and. Operators. 1. Introduction The CauchyProblem, Local Dependence In this chapter, ... Since the theory of linear

**partial**differential operators is vast and highly ramified, we shall only touch upon a

number of ...

Page 1633

A third category of formal

the operator 8 82 8xv 8x\ This sort of operator is closely related to the theory of

semi-groups, where we have already seen general equations of the form d- T(t)f ...

A third category of formal

**partial**differential operators is the parabolic, typified bythe operator 8 82 8xv 8x\ This sort of operator is closely related to the theory of

semi-groups, where we have already seen general equations of the form d- T(t)f ...

Page 1703

The Elliptic Boundary Value Problem Can the boundary value theory and the

spectral theory of Chapter XIII be generalized to

the present section it will be seen that it can, at least for the class of elliptic

...

The Elliptic Boundary Value Problem Can the boundary value theory and the

spectral theory of Chapter XIII be generalized to

**partial**differential operators? Inthe present section it will be seen that it can, at least for the class of elliptic

**partial**...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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### Common terms and phrases

Acad adjoint extension adjoint operator algebra Amer analytic B*-algebra Banach spaces Borel set boundary conditions boundary values bounded operator closed closure coefficients complex numbers constant continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function q Haar measure Hence Hilbert space Hilbert-Schmidt operator hypothesis identity inequality integral interval kernel Lemma linear operator linearly independent mapping matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma Proc prove real axis real numbers representation satisfies Section sequence singular solution spectral spectral theory square-integrable subspace Suppose symmetric operator theory topology transform unique unitary vanishes vector zero