## Linear Operators: Spectral theory |

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Page 937

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle.

CHAPTER XI Miscellaneous Applications This chapter is devoted to applications

of the spectral

mathematics.

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle.

CHAPTER XI Miscellaneous Applications This chapter is devoted to applications

of the spectral

**theory**of normal operators to problems in a variety of fields ofmathematics.

Page 1435

Thus, in all cases in which we deal with a formal differential operator on an

interval I having coefficients analytic in I and with poles at the free end points of I,

the

of ...

Thus, in all cases in which we deal with a formal differential operator on an

interval I having coefficients analytic in I and with poles at the free end points of I,

the

**theory**of regular and irregular singularities enables us to reduce the problemof ...

Page 1645

Hence, we are led to the attempt to define some sort of “generalized function.” A

very complete and interesting development of such a

functions was given by Laurent Schwartz; the generalized functions were called

by ...

Hence, we are led to the attempt to define some sort of “generalized function.” A

very complete and interesting development of such a

**theory**of generalizedfunctions was given by Laurent Schwartz; the generalized functions were called

by ...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Spectral Representation | 909 |

Copyright | |

17 other sections not shown

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### Common terms and phrases

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