## Linear Operators: Spectral operators |

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Page 2029

Similarly , functions on RN may

sometimes

equivalent to the statement that for any two polynomials P , Q in N variables we

have ...

Similarly , functions on RN may

**determine**tempered distributions just as theysometimes

**determine**distributions . For example , since convergence Pn in 0 isequivalent to the statement that for any two polynomials P , Q in N variables we

have ...

Page 2184

It will be seen in the following 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

It will be seen in the following 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**...Page 2316

Hence , in can only be a multiple pole of the resolvent of T if Pn ( t ) ) 2 Do dt = 0 .

Now , we have on ( t ) = sin sn ( t + an ) = sin ( snt + Br ) , where Bn must be

něko ) ...

Hence , in can only be a multiple pole of the resolvent of T if Pn ( t ) ) 2 Do dt = 0 .

Now , we have on ( t ) = sin sn ( t + an ) = sin ( snt + Br ) , where Bn must be

**determined**so as to satisfy kölsn sin Bn = cos Bn . It follows readily that Br = - (něko ) ...

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### Contents

SPECTRAL OPERATORS | 1924 |

An Operational Calculus for Bounded Spectral | 1941 |

Part | 1950 |

Copyright | |

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