## Linear Operators: Spectral operators |

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Page 937

CHAPTER XI Miscellaneous Applications This chapter is devoted to applications

of the spectral

mathematics. Since these topics are not in the main stream of our interest we

shall ...

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. Since these topics are not in the main stream of our interest we

shall ...

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 1815

Amer. Math. Soc. 55, 1015–1034 (1949). Measure

York, 1950. Introduction to Hilbert space and the

Chelsea, New York, 1951. Finite dimensional vector spaces. Ann. of Math. Stud.

Amer. Math. Soc. 55, 1015–1034 (1949). Measure

**Theory**. D. van Nostrand, NewYork, 1950. Introduction to Hilbert space and the

**theory**of spectral multiplicity.Chelsea, New York, 1951. Finite dimensional vector spaces. Ann. of Math. Stud.

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

4 Exercises | 879 |

Copyright | |

52 other sections not shown

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### Common terms and phrases

adjoint extension adjoint operator algebra analytic B-algebra B-space Borel set boundary conditions boundary values bounded operator closed closure Cº(I coefficients compact operator complex numbers constant continuous function converges Corollary deficiency indices Definition denote dense domain eigenfunctions eigenvalues element equation essential spectrum Exercise exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Hence Hilbert space Hilbert-Schmidt operator identity inequality infinity integral interval kernel Lemma Let f Let Q linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma prove real numbers satisfies sequence singular ſº solution spectral spectral theorem square-integrable subspace Suppose symmetric operator theory To(r To(t topology transform uniformly unique unitary vanishes vector zero