2,716 research outputs found
Wavelet frame bijectivity on Lebesgue and Hardy spaces
We prove a sufficient condition for frame-type wavelet series in , the
Hardy space , and BMO. For example, functions in these spaces are shown to
have expansions in terms of the Mexican hat wavelet, thus giving a strong
answer to an old question of Meyer.
Bijectivity of the wavelet frame operator acting on Hardy space is
established with the help of new frequency-domain estimates on the
Calder\'on-Zygmund constants of the frame kernel.Comment: 23 pages, 7 figure
Marcinkiewicz-Zygmund inequalities
We study a generalization of the classical Marcinkiewicz-Zygmund
inequalities. We relate this problem to the sampling sequences in the
Paley-Wiener space and by using this analogy we give sharp necessary and
sufficient computable conditions for a family of points to satisfy the
Marcinkiewicz-Zygmund inequalities
An application of the effective Sato-Tate conjecture
Based on the Lagarias-Odlyzko effectivization of the Chebotarev density
theorem, Kumar Murty gave an effective version of the Sato-Tate conjecture for
an elliptic curve conditional on analytic continuation and Riemann hypothesis
for the symmetric power -functions. We use Murty's analysis to give a
similar conditional effectivization of the generalized Sato-Tate conjecture for
an arbitrary motive. As an application, we give a conditional upper bound of
the form for the smallest prime at which two
given rational elliptic curves with conductor at most have Frobenius traces
of opposite sign.Comment: 12 pages; v2: refereed versio
Oscillation and the mean ergodic theorem for uniformly convex Banach spaces
Let B be a p-uniformly convex Banach space, with p >= 2. Let T be a linear
operator on B, and let A_n x denote the ergodic average (1 / n) sum_{i< n} T^n
x. We prove the following variational inequality in the case where T is power
bounded from above and below: for any increasing sequence (t_k)_{k in N} of
natural numbers we have sum_k || A_{t_{k+1}} x - A_{t_k} x ||^p <= C || x ||^p,
where the constant C depends only on p and the modulus of uniform convexity.
For T a nonexpansive operator, we obtain a weaker bound on the number of
epsilon-fluctuations in the sequence. We clarify the relationship between
bounds on the number of epsilon-fluctuations in a sequence and bounds on the
rate of metastability, and provide lower bounds on the rate of metastability
that show that our main result is sharp
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