## Linear Operators: Spectral theory |

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Page 1249

Thus PP* is a projection whose range is 92 = Post, the final domain of P. To

complete the proof it will suffice to show that P*P is a projection if P is a

isometry. Let a, ve)', the initial domain of P. Then the identity r +v? = |Pr-i-Pul”

shows that ...

Thus PP* is a projection whose range is 92 = Post, the final domain of P. To

complete the proof it will suffice to show that P*P is a projection if P is a

**partial**isometry. Let a, ve)', the initial domain of P. Then the identity r +v? = |Pr-i-Pul”

shows that ...

Page 1629

CHAPTER XIV Linear

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

variety of theorems having to do with linear

the ...

CHAPTER XIV Linear

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

variety of theorems having to do with linear

**partial**differential operators. Sincethe ...

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 |

Spectral Representation | 909 |

Copyright | |

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adjoint extension adjoint operator algebra Amer analytic B-algebra Banach Borel set boundary conditions boundary values bounded operator closed closure Cº(I coefficients complete complex numbers 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 f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval kernel Lemma Let f linear operator linearly independent mapping Math matrix measure Nauk SSSR N.S. neighborhood norm open set operators in Hilbert orthogonal orthonormal Plancherel's theorem positive Proc PRoof prove real numbers satisfies sequence singular ſº solution spectral spectral set spectral theory square-integrable subspace Suppose theory To(r topology transform unique unitary vanishes vector zero