133,583 research outputs found
Littlewood-Paley-Stein type square functions based on Laguerre semigroups
We investigate g-functions based on semigroups related to multi-dimensional
Laguerre function expansions of convolution type. We prove that these operators
can be viewed as Calderon-Zygmund operators in the sense of the underlying
space of homogeneous type, hence their mapping properties follow from the
general theory.Comment: 30 page
Transcendence measures and algebraic growth of entire functions
In this paper we obtain estimates for certain transcendence measures of an
entire function . Using these estimates, we prove Bernstein, doubling and
Markov inequalities for a polynomial in along the graph
of . These inequalities provide, in turn, estimates for the number of zeros
of the function in the disk of radius , in terms of the degree
of and of .
Our estimates hold for arbitrary entire functions of finite order, and
for a subsequence of degrees of polynomials. But for special classes
of functions, including the Riemann -function, they hold for all degrees
and are asymptotically best possible. From this theory we derive lower
estimates for a certain algebraic measure of a set of values , in terms
of the size of the set .Comment: 40 page
Large Bergman spaces: invertibility, cyclicity, and subspaces of arbitrary index
In a wide class of weighted Bergman spaces, we construct invertible
non-cyclic elements. These are then used to produce z-invariant subspaces of
index higher than one. In addition, these elements generate nontrivial
bilaterally invariant subspaces in anti-symmetrically weighted Hilbert spaces
of sequences.Comment: 40 page
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