## Linear Operators: Spectral operators |

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Page 2118

A generalized scalar operator Te B ( X ) is said to be

A generalized scalar operator Te B ( X ) is said to be

**regular**if it has a**regular**spectral distribution . Although it is not known whether or not every generalized scalar operator is**regular**( unless the spectrum is sufficiently “ thin ...Page 2158

If the set of points

If the set of points

**regular**relative to T is dense on To , then every closed subinterval of whose end points are**regular**relative to T is in S ( T ) and every Borel subset of the plane is measurable T. PROOF .Page 2344

Then all the conclusions of Theorem 8 are valid . this connection , it is also worth making a simple remark on the notion of

Then all the conclusions of Theorem 8 are valid . this connection , it is also worth making a simple remark on the notion of

**regular**boundary conditions in the case of a second order differential operator . If the boundary conditions ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

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adjoint operator Amer analytic apply arbitrary assumed B-space Banach space belongs Boolean algebra Borel set boundary conditions bounded bounded operator Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension fact finite follows formal formula function given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear operator Math Moreover multiplicity norm perturbation plane positive preceding present problem projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type seen sequence shown shows similar solution spectral measure spectral operator spectrum subset sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero