Linear Operators: Spectral operators |
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Page 2068
It is clear that the linear space Lo = Lin Lo satisfies ( 11 ) . Also the space Lo = Lin
C of all integrable functions which coincide almost everywhere with a continuous
function clearly satisfies ( 11 ) . Example 11 . 12 shows that the space Lo = Lin ...
It is clear that the linear space Lo = Lin Lo satisfies ( 11 ) . Also the space Lo = Lin
C of all integrable functions which coincide almost everywhere with a continuous
function clearly satisfies ( 11 ) . Example 11 . 12 shows that the space Lo = Lin ...
Page 2112
The proof of this theorem is based on an analysis of certain B - spaces of vector
valued analytic functions . We say that T satisfies condition ( B ) if for every open
set U and every sequence { fr } of analytic functions from U to X and X e X such ...
The proof of this theorem is based on an analysis of certain B - spaces of vector
valued analytic functions . We say that T satisfies condition ( B ) if for every open
set U and every sequence { fr } of analytic functions from U to X and X e X such ...
Page 2314
This satisfies the boundary condition at t = 0 if tan sa = ko 8 , and satisfies the
boundary conditions at t = 1 if tan s ( 1 + x ) = k18 . Thus , using the addition
formula for the tangent function , T - XI can only fail to have an inverse if = sa ,
where s is ...
This satisfies the boundary condition at t = 0 if tan sa = ko 8 , and satisfies the
boundary conditions at t = 1 if tan s ( 1 + x ) = k18 . Thus , using the addition
formula for the tangent function , T - XI can only fail to have an inverse if = sa ,
where s is ...
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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