This is an announcement for the paper "Approximating with Gaussians"
by Craig Calcaterra and Axel Boldt.
Abstract: Linear combinations of translations of a single Gaussian,
e^{-x^2}, are shown to be dense in L^2(R). Two algorithms for determining
the coefficients for the approximations are given, using orthogonal
Hermite functions and least squares. Taking the Fourier transform of
this result shows low-frequency trigonometric series are dense in L^2
with Gaussian weight function.
Archive classification: math.CA math.FA
Mathematics Subject Classification: 41A30; 42A32; 42C10
Remarks: 16 pages, 23 figures
The source file(s), AppGaussArXiv3.tex: 61111 bytes I100.png: 14299
bytes I200.png: 7466 bytes I210.png: 8594 bytes I220.png: 8450 bytes
I230.png: 9254 bytes I240.png: 8799 bytes I250.png: 8967 bytes I300.png:
8446 bytes I310.png: 10845 bytes I311.png: 10945 bytes I320.png: 10846
bytes I330.png: 11696 bytes I340.png: 11710 bytes I350.png: 11061 bytes
I400.png: 10444 bytes I410.png: 10145 bytes I420.png: 9810 bytes I500.png:
10246 bytes I510.png: 10478 bytes I520.png: 11634 bytes I530.png: 11233
bytes I600.png: 10241 bytes I610.png: 11497 bytes, is(are) stored in
gzipped form as 0805.3795.tar.gz with size 202kb. The corresponding
postcript file has gzipped size 279kb.
Submitted from: axel.boldt(a)metrostate.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0805.3795
or
http://arXiv.org/abs/0805.3795
or by email in unzipped form by transmitting an empty message with
subject line
uget 0805.3795
or in gzipped form by using subject line
get 0805.3795
to: math(a)arXiv.org.
This is an announcement for the paper "On distribution and almost
convergence of bounded sequences" by Chao You and Bao Qi Feng.
Abstract: In this paper, we give the concepts of properly distributed
and simply distributed sequences, and prove that they are almost
convergent. Basing on these, we review the work of Feng and Li
[Feng, B. Q. and Li, J. L., Some estimations of Banach limits,
J. Math. Anal. Appl. 323(2006) No. 1, 481-496. MR2262220 46B45 (46A45).],
which is shown to be a special case of our generalized theory.
Archive classification: math.FA math.GM
Mathematics Subject Classification: Primary 40G05, 46A35, 54A20;
Secondary 11K36
Remarks: 8 pages
The source file(s),
Ondistributionandalmostconvergenceofboundedsequences.tex: 25039 bytes,
is(are) stored in gzipped form as 0805.3950.gz with size 8kb. The
corresponding postcript file has gzipped size 68kb.
Submitted from: hityou1982(a)gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0805.3950
or
http://arXiv.org/abs/0805.3950
or by email in unzipped form by transmitting an empty message with
subject line
uget 0805.3950
or in gzipped form by using subject line
get 0805.3950
to: math(a)arXiv.org.
This is an announcement for the paper "On the nontrivial projection
problem" by Stanislaw J. Szarek and Nicole Tomczak-Jaegermann.
Abstract: The Nontrivial Projection Problem asks whether every
finite-dimensional normed space of dimension greater than one admits a
well-bounded projection of non-trivial rank and corank or, equivalently,
whether every centrally symmetric convex body (of arbitrary dimension
greater than one) is approximately affinely equivalent to a direct product
of two bodies of non-trivial dimension. We show that this is true "up
to a logarithmic factor."
Archive classification: math.FA
Mathematics Subject Classification: 46B20, secondary 46B07, 52A21
Remarks: 17 pages
The source file(s), NPPforArxiv.tex: 46100 bytes, is(are) stored in
gzipped form as 0805.3792.gz with size 17kb. The corresponding postcript
file has gzipped size 126kb.
Submitted from: szarek(a)cwru.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0805.3792
or
http://arXiv.org/abs/0805.3792
or by email in unzipped form by transmitting an empty message with
subject line
uget 0805.3792
or in gzipped form by using subject line
get 0805.3792
to: math(a)arXiv.org.
This is an announcement for the paper "Simultaneous realization of
function space structures in transitive Banach spaces" by Fernando
Rambla and Jarno Talponen.
Abstract: Let L be a locally compact Hausdorff space and m the Lebesgue
measure on the unit interval. We will prove the existence of a transitive
Banach space X such that C_{0}(L,X) and the Bochner spaces L^{p}(m,X),
1\leq p\leq \infty, are all isometrically isomorphic to X. Also, more
general results of this type are presented.
Archive classification: math.FA
Mathematics Subject Classification: 46B04; 46E40
The source file(s), BCO4.tex: 52768 bytes, is(are) stored in gzipped
form as 0805.3616.gz with size 15kb. The corresponding postcript file
has gzipped size 96kb.
Submitted from: talponen(a)cc.helsinki.fi
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0805.3616
or
http://arXiv.org/abs/0805.3616
or by email in unzipped form by transmitting an empty message with
subject line
uget 0805.3616
or in gzipped form by using subject line
get 0805.3616
to: math(a)arXiv.org.
This is an announcement for the paper "The least singular value of a
random square matrix is O(n^{-1/2})" by Mark Rudelson and Roman Vershynin.
Abstract: Let A be a matrix whose entries are real i.i.d. centered random
variables with unit variance and suitable moment assumptions. Then
the smallest singular value of A is of order n^{-1/2} with high
probability. The lower estimate of this type was proved recently by the
authors; in this note we establish the matching upper estimate.
Archive classification: math.PR math.FA
Mathematics Subject Classification: 15A52
Remarks: 6 pages
The source file(s), square-matrices-reverse.tex: 17210 bytes, is(are)
stored in gzipped form as 0805.3407.gz with size 6kb. The corresponding
postcript file has gzipped size 68kb.
Submitted from: vershynin(a)math.ucdavis.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0805.3407
or
http://arXiv.org/abs/0805.3407
or by email in unzipped form by transmitting an empty message with
subject line
uget 0805.3407
or in gzipped form by using subject line
get 0805.3407
to: math(a)arXiv.org.
This is an announcement for the paper "A note on James spaces and
superstrictly singular operators" by Isabelle Chalendar, Emmanuel Fricain,
and Dan Timotin.
Abstract: An elementary lemma is used in order to show that the natural
inclusion $J_p\to J_q$ of James spaces is superstrictly singular for
$p<q$. As a consequence, it is shown that an operator without nontrivial
invariant subspaces constructed by Charles Read is superstrictly singular.
Archive classification: math.FA
The source file(s), James.tex: 20594 bytes, is(are) stored in gzipped
form as 0805.3409.gz with size 7kb. The corresponding postcript file
has gzipped size 70kb.
Submitted from: fricain(a)math.univ-lyon1.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0805.3409
or
http://arXiv.org/abs/0805.3409
or by email in unzipped form by transmitting an empty message with
subject line
uget 0805.3409
or in gzipped form by using subject line
get 0805.3409
to: math(a)arXiv.org.
Dear Colleagues,
We would like to invite you to participate in the summer school on
"Fourier analytic and probabilistic methods in geometric functional
analysis and convexity" in August 13-20, 2008.
The school is being organized by the NSF funded Focused Research Group
collaborative project on the same subject
(http://www.math.ucdavis.edu/~geofunction/). It is oriented towards
graduate students, postdocs and researchers who wish to get an
introduction to the subject. The school will feature several series's
of lectures. Confirmed speakers include
Alexander Barvinok (University of Michigan),
Piotr Indyk (Massachusetts Institute of Technology),
Fedor Nazarov (University of Wisconsin-Madison),
Krzysztof Oleszkiewicz (University of Warsaw),
Gideon Schechtman (Weizmann Institute of Scince),
Rolf Schneider (University of Freiburg),
Mikhail Sodin (Tel Aviv University),
Santosh S. Vempala (Georgia Institute of Technology).
The school will be hosted by the Department of Mathematical Sciences at
Kent State University in August 13-20, 2008 (Arrival date: August 12/
Departure Date August 21). Kent is located in the suburbs of Cleveland,
Ohio, where summers are quite beautiful.
For further information and breaking news, please, consult
http://www.math.kent.edu/math/FAPR.cfm
and e-mail to to Dmitry Ryabogin (ryabogin(a)math.kent.edu) or Artem
Zvavitch (zvavitch(a)math.kent.edu).
We hope to see you in Kent next August.
Best Regards,
The organizing committee
Alex Koldobsky
Mark Rudelson
Dmitry Ryabogin
Stanislaw Szarek
Roman Vershynin
Elisabeth Werner
Artem Zvavitch
This is an announcement for the paper "On unconditionally saturated
Banach spaces" by Pandelis Dodos and Jordi Lopez-Abad.
Abstract: We prove a structural property of the class of unconditionally
saturated separable Banach spaces. We show, in particular, that for every
analytic set $\aaa$, in the Effros-Borel space of subspaces of $C[0,1]$,
of unconditionally saturated separable Banach spaces, there exists
an unconditionally saturated Banach space $Y$, with a Schauder basis,
that contains isomorphic copies of every space $X$ in the class $\aaa$.
Archive classification: math.FA math.LO
Mathematics Subject Classification: 03E15, 46B03, 46B07, 46B15
Remarks: 16 pages, no figures. Studia Mathematica (to appear)
The source file(s), UnconditionallySaturated-ArXiv.tex: 49281 bytes,
is(are) stored in gzipped form as 0805.2046.gz with size 14kb. The
corresponding postcript file has gzipped size 102kb.
Submitted from: pdodos(a)math.ntua.gr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0805.2046
or
http://arXiv.org/abs/0805.2046
or by email in unzipped form by transmitting an empty message with
subject line
uget 0805.2046
or in gzipped form by using subject line
get 0805.2046
to: math(a)arXiv.org.
This is an announcement for the paper "On classes of Banach spaces
admitting ``small" universal spaces" by Pandelis Dodos.
Abstract: We characterize those classes $\ccc$ of separable Banach
spaces admitting a separable universal space $Y$ (that is, a space $Y$
containing, up to isomorphism, all members of $\ccc$) which is not
universal for all separable Banach spaces. The characterization is a
byproduct of the fact, proved in the paper, that the class $\mathrm{NU}$
of non-universal separable Banach spaces is strongly bounded. This settles
in the affirmative the main conjecture form \cite{AD}. Our approach
is based, among others, on a construction of $\llll_\infty$-spaces,
due to J. Bourgain and G. Pisier. As a consequence we show that there
exists a family $\{Y_\xi:\xi<\omega_1\}$ of separable, non-universal,
$\llll_\infty$-spaces which uniformly exhausts all separable Banach
spaces. A number of other natural classes of separable Banach spaces
are shown to be strongly bounded as well.
Archive classification: math.FA math.LO
Mathematics Subject Classification: 03E15, 46B03, 46B07, 46B15
Remarks: 25 pages, no figures
The source file(s), Universal-ArXiv.tex: 81806 bytes, is(are) stored in
gzipped form as 0805.2043.gz with size 24kb. The corresponding postcript
file has gzipped size 143kb.
Submitted from: pdodos(a)math.ntua.gr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0805.2043
or
http://arXiv.org/abs/0805.2043
or by email in unzipped form by transmitting an empty message with
subject line
uget 0805.2043
or in gzipped form by using subject line
get 0805.2043
to: math(a)arXiv.org.
This is an announcement for the paper "On antichains of spreading models
of Banach spaces" by Pandelis Dodos.
Abstract: We show that for every separable Banach space $X$, either
$\spw(X)$ (the set of all spreading models of $X$ generated by weakly-null
sequences in $X$, modulo equivalence) is countable, or $\spw(X)$ contains
an antichain of the size of the continuum. This answers a question of
S. J. Dilworth, E. Odell and B. Sari.
Archive classification: math.FA math.LO
Mathematics Subject Classification: 03E15, 46B20
Remarks: 14 pages, no figures. Canadian Mathematical Bulletin (to appear)
The source file(s), SP-ArXiv.tex: 44752 bytes, is(are) stored in gzipped
form as 0805.2038.gz with size 13kb. The corresponding postcript file
has gzipped size 96kb.
Submitted from: pdodos(a)math.ntua.gr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0805.2038
or
http://arXiv.org/abs/0805.2038
or by email in unzipped form by transmitting an empty message with
subject line
uget 0805.2038
or in gzipped form by using subject line
get 0805.2038
to: math(a)arXiv.org.