## Linear Operators: Spectral operators |

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A scalar function y on RN is said to

A scalar function y on RN is said to

**determine**the tempered distribution T , in RN if for every q in 0 , Q ( ) ( s ) is Lebesgue integrable on RN and the functional Tv defined by the equation ( 49 ) Tv ( 9 ) ) = S 90 ( 8 ) 4 ( s ) ...Page 2184

... theorem that an arbitrary isomorphic homeomorphism of the algebra A ( B ) onto the algebra of continuous functions on its structure space may be represented by an integral with respect to a uniquely

... theorem that an arbitrary isomorphic homeomorphism of the algebra A ( B ) onto the algebra of continuous functions on its structure space may be represented by an integral with respect to a uniquely

**determined**spectral measure .Page 2316

Hence , in can only be a multiple pole of the resolvent of T if S ( 92 ( e ) ? dt = 0 . Now , we have Pr ( t ) = sin sn ( t + cm ) = sin ( snt + Br ) , where Bn must be

Hence , in can only be a multiple pole of the resolvent of T if S ( 92 ( e ) ? dt = 0 . Now , we have Pr ( t ) = sin sn ( t + cm ) = sin ( snt + Br ) , where Bn must be

**determined**so as to satisfy kö sn sin Bn = cos Br . It follows ...### 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 | |

32 other sections not shown

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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