S. J. Dilworth
Explicit constructions of RIP matrices and related problems.
Пт, 08/27/2010 - 15:02 — SomNambulAuthors: S. J. Dilworth, Jean Bourgain, Kevin Ford, Sergei Konyagin, Denka Kutzarova
Subjects: Number Theory
AbstractWe give a new explicit construction of $n\times N$ matrices satisfying the
Restricted Isometry Property (RIP). Namely, for some c>0, large N and any n
satisfying N^{1-c} < n < N, we construct RIP matrices of order k^{1/2+c}. This
overcomes the natural barrier k=O(n^{1/2}) for proofs based on small coherence,
which are used in all previous explicit constructions of RIP matrices. Key
ingredients in our proof are new estimates for sumsets in product sets and for
exponential sums with the products of sets possessing special additive
structure.- Читать далее
- 1 комментарий
- login or register to post comments
Greedy bases for Besov spaces.
Ср, 10/21/2009 - 14:15 — SomNambulAuthors: S. J. Dilworth, D. Freeman, E. Odell, Th. Schlumprecht
Subjects: Functional Analysis
AbstractWe prove thatthe Banach space $(\oplus_{n=1}^\infty \ell_p^n)_{\ell_q}$,
which is isomorphic to certain Besov spaces, has a greedy basis whenever $1\leq
p \leq\infty$ and $1<q<\infty$. Furthermore, the Banach spaces
$(\oplus_{n=1}^\infty \ell_p^n)_{\ell_1}$, with $1<p\le \infty$, and
$(\oplus_{n=1}^\infty \ell_p^n)_{c_0}$, with $1\le p<\infty$ do not have a
greedy bases. We prove as well that the space $(\oplus_{n=1}^\infty
\ell_p^n)_{\ell_q}$ has a 1-greedy basis if and only if $1\leq p=q\le \infty$.Greedy bases for Besov spaces.
Ср, 10/21/2009 - 14:15 — SomNambulAuthors: S. J. Dilworth, D. Freeman, E. Odell, Th. Schlumprecht
Subjects: Functional Analysis
AbstractWe prove thatthe Banach space $(\oplus_{n=1}^\infty \ell_p^n)_{\ell_q}$,
which is isomorphic to certain Besov spaces, has a greedy basis whenever $1\leq
p \leq\infty$ and $1<q<\infty$. Furthermore, the Banach spaces
$(\oplus_{n=1}^\infty \ell_p^n)_{\ell_1}$, with $1<p\le \infty$, and
$(\oplus_{n=1}^\infty \ell_p^n)_{c_0}$, with $1\le p<\infty$ do not have a
greedy bases. We prove as well that the space $(\oplus_{n=1}^\infty
\ell_p^n)_{\ell_q}$ has a 1-greedy basis if and only if $1\leq p=q\le \infty$.
Вход в систему
