1,069 research outputs found
On a space of entire functions rapidly decreasing on and its Fourier transformation
A space of entire functions of several complex variables rapidly decreasing
on and such that their growth along is
majorized with a help of a family of weight functions is considered in the
paper. For this space an equivalent description in terms of estimates on all
partial derivatives of functions on and Paley-Wiener type
theorem are obtained.Comment: 20 page
On a Fr\'echet space of entire functions rapidly decreasing on the real line
A weighted space of entire functions rapidly decreasing on the real line is
considered in the paper. A growth of these functions along the imaginary axis
is controlled by some system of weight functions. The Fourier transform of
functions of this space is studied. Equivalent description of the considered
space in terms of estimates on derivatives of functions on real line is
obtained.Comment: 16 page
On weighted polynomial approximation
Let be a semi-continuous from below
function such that . It is shown that polynomials are dense
in
An extension the semidefinite programming bound for spherical codes
In this paper we present an extension of known semidefinite and linear
programming upper bounds for spherical codes and consider a version of this
bound for distance graphs. We apply the main result for the distance
distribution of a spherical code.Comment: 11 page
Around Sperner's lemma
We consider a generalization of the classic Sperner lemma. This lemma states
that every Sperner coloring of a triangulation of a simplex contains a fully
colored simplex. We found a weaker assumption than Sperner's coloring. It is
also shown that the main theorem implies Tucker's lemma and some other
theorems.Comment: 15 pages, 6 figures. arXiv admin note: text overlap with
arXiv:1212.189
On rigid Hirzebruch genera
The classical multiplicative (Hirzebruch) genera of manifolds have the
wonderful property which is called rigidity. Rigidity of a genus h means that
if a compact connected Lie group G acts on a manifold X, then the equivariant
genus h^G(X) is independent on G, i.e. h^G(X)=h(X). In this paper we are
considering the rigidity problem for complex manifolds. In particular, we are
proving that a genus is rigid if and only if it is a generalized Todd genus.Comment: 10 page
Ramanujan's theorem and highest abundant numbers
In 1915, Ramanujan proved asymptotic inequalities for the sum of divisors
function, assuming the Riemann hypothesis (RH). We consider a strong version of
Ramanujan's theorem and define highest abundant numbers that are extreme with
respect to the Ramanujan and Robin inequalities. Properties of these numbers
are very different depending on whether the RH is true or false.Comment: 12 pages, 1 figur
Minimal Spinning String
Minimal N=1/2 supersymmetric extension of bosonic Polyakov's string is
constructed. This model is natural generalization of Di Vecchia-Ravndal
superparticle. The classical sector of the model is investigated, Noether
currents and Virosoro supercondition are found. Minimal spinning string is more
simple, than the standard N=1 spinning string of Neveu-Schwarz-Ramond and has a
number of unusial properties such as a chiral symmetry, parabolic type of
equations of movement, non-triviality fermionic sectors for closed strings only
and e.t.c.Comment: LaTeX 2.09 (twice), 5 pages, Talk given on 9th Russ. Grav. Conf.
Novgorod, 24-30 June 199
Bounds for Codes by Semidefinite Programming
Delsarte's method and its extensions allow to consider the upper bound
problem for codes in 2-point-homogeneous spaces as a linear programming problem
with perhaps infinitely many variables, which are the distance distribution. We
show that using as variables power sums of distances this problem can be
considered as a finite semidefinite programming problem. This method allows to
improve some linear programming upper bounds. In particular we obtain new
bounds of one-sided kissing numbers.Comment: 20 page
Circle actions with two fixed points
We prove that if the circle group acts smooth and unitary on 2n-dimensional
stably complex manifold with two isolated fixed points and it is not bound
equivariantly, then n=1 or 3. Our proof relies on the rigid Hirzebruch genera
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