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Extreme positive definite double sequences which are not moment sequences.

Torben Maack Bisgaard (2003)

Collectanea Mathematica

From the fact that the two-dimensional moment problem is not always solvable, we can deduce that there must be extreme ray generators of the cone of positive definite double sequences which are nor moment sequences. Such an argument does not lead to specific examples. In this paper it is shown how specific examples can be constructed if one is given an example of an N-extremal indeterminate measure in the one-dimensional moment problem (such examples exist in the literature). Konrad Schmüdgen had...

Fourier coefficients of continuous functions and a class of multipliers

Serguei V. Kislyakov (1988)

Annales de l'institut Fourier

If x is a bounded function on Z , the multiplier with symbol x (denoted by M x ) is defined by ( M x f ) ^ = x f ^ , f L 2 ( T ) . We give some conditions on x ensuring the “interpolation inequality” M x f L p C f L 1 α M x f L q 1 - α (here 1 < p < q and α = α ( p , q , x ) is between 0 and 1). In most cases considered M x fails to have stronger L 1 -regularity properties (e.g. fails to be of weak type (1,1)). The results are applied to prove that for many sets E Z every positive sequence in 2 ( E ) can be majorized by the sequence { ...

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