Results 11 to 20 of about 116 (41)
Singular measures and convolution operators
, 2002 We show that in the study of certain convolution operators, functions can be replaced by measures without changing the size of the constants appearing in weak type (1,1) inequalities.
Aldaz +8 more
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Approximate identities on some homogeneous Banach spaces [PDF]
, 2009 We study the geometric and approximation properties of Marcinkiewicz spaces and Stepanoff spaces, $1 \leq p < \infty$, as well as others where translations are not isometric but bounded (the bounded $p$-mean spaces) or even unbounded ($\Mean0$).
Andreano, F, Picardello, AM
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Convolution Powers of Salem Measures with Applications [PDF]
, 2015 We study the regularity of convolution powers for measures supported on Salem sets, and prove related results on Fourier restriction and Fourier multipliers. In particular we show that for $\alpha$ of the form ${d}/{n}, n=2,3,\cdots$ there exist $\alpha$-
Chen, Xianghong, Seeger, Andreas
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Growth rate for beta-expansions
, 2009 Let $\beta>1$ and let $m>\be$ be an integer. Each $x\in I_\be:=[0,\frac{m-1}{\beta-1}]$ can be represented in the form \[ x=\sum_{k=1}^\infty \epsilon_k\beta^{-k}, \] where $\epsilon_k\in\{0,1,...,m-1\}$ for all $k$ (a $\beta$-expansion of $x$).
Feng, De-Jun, Sidorov, Nikita
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Advanced Nonlinear StudiesWe consider nonlocal differential equations with convolution coefficients of the form−M(a*|u|q)(1)μ(t)u″(t)=λft,u(t), t∈(0,1), $$-M\left(\left(a {\ast} \vert u{\vert }^{q}\right)\left(1\right)\mu \left(t\right)\right){u}^{{\prime\prime}}\left(t\right ...
Goodrich Christopher S.
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The supremum of autoconvolutions, with applications to additive number theory [PDF]
, 2009 We adapt a number-theoretic technique of Yu to prove a purely analytic theorem: if f(x) is in L^1 and L^2, is nonnegative, and is supported on an interval of length I, then the supremum of the convolution f*f is at least 0.631 \| f \|_1^2 / I.
Martin, Greg, O'Bryant, Kevin
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A topological analysis of p(x)-harmonic functionals in one-dimensional nonlocal elliptic equations
Advanced Nonlinear StudiesWe consider a class of one-dimensional elliptic equations possessing a p(x)-harmonic functional as a nonlocal coefficient.
Goodrich Christopher S.
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Continuity of LF-algebra representations associated to representations of Lie groups
, 2012 Let G be a Lie group and E be a locally convex topological G-module. If E is sequentially complete, then E and its space of smooth vectors are modules for the algebra D(G) of compactly supported smooth functions on G. However, the module multiplication
Glockner, Helge
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Spectral measures associated with the factorization of the Lebesgue measure on a set via convolution [PDF]
, 2013 Let $Q$ be a fundamental domain of some full-rank lattice in ${\Bbb R}^d$ and let $\mu$ and $\nu$ be two positive Borel measures on ${\Bbb R}^d$ such that the convolution $\mu\ast\nu$ is a multiple of $\chi_Q$.
Gabardo, Jean-Pierre, Lai, Chun-Kit
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Scaling by 5 on a 1/4-Cantor Measure [PDF]
, 2012 Each Cantor measure (\mu) with scaling factor 1/(2n) has at least one associated orthonormal basis of exponential functions (ONB) for L^2(\mu). In the particular case where the scaling constant for the Cantor measure is 1/4 and two specific ONBs are ...
B. Arveson +5 more
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