Linear Operators, Part 2 |
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Page 1019
Nelson Dunford, Jacob T. Schwartz. volume of any n - sided parallelepiped is
never larger than the volume of a rectangular parallelepiped with sides of the
same lengths . Proof . The inequality is obvious for n = 1 and may be easily
checked ...
Nelson Dunford, Jacob T. Schwartz. volume of any n - sided parallelepiped is
never larger than the volume of a rectangular parallelepiped with sides of the
same lengths . Proof . The inequality is obvious for n = 1 and may be easily
checked ...
Page 1061
14 ) and Hölder ' s inequality , and the theorem is proved for all p , 1 < p < 0 . Q . E
. D . Having proved the basic inequality of M . Riesz , we now proceed to prove
the full inequality of Calderón and Zygmund . Our first step is to put the result of ...
14 ) and Hölder ' s inequality , and the theorem is proved for all p , 1 < p < 0 . Q . E
. D . Having proved the basic inequality of M . Riesz , we now proceed to prove
the full inequality of Calderón and Zygmund . Our first step is to put the result of ...
Page 1105
We now pause to sharpen another of the inequalities of Lemma 9 . ... the
continuity of the product TS which was noted in the paragraph following Lemma 9
, the continuity of the norm function which follows from the triangle inequality of
Lemma ...
We now pause to sharpen another of the inequalities of Lemma 9 . ... the
continuity of the product TS which was noted in the paragraph following Lemma 9
, the continuity of the norm function which follows from the triangle inequality of
Lemma ...
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Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
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additive adjoint operator algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense derivatives determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function give given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero