7,569 research outputs found

### Estimates in Beurling--Helson type theorems. Multidimensional case

We consider the spaces $A_p(\mathbb T^m)$ of functions $f$ on the $m$
-dimensional torus $\mathbb T^m$ such that the sequence of the Fourier
coefficients $\hat{f}=\{\hat{f}(k), ~k \in \mathbb Z^m\}$ belongs to
$l^p(\mathbb Z^m), ~1\leq p<2$. The norm on $A_p(\mathbb T^m)$ is defined by
$\|f\|_{A_p(\mathbb T^m)}=\|\hat{f}\|_{l^p(\mathbb Z^m)}$. We study the rate of
growth of the norms $\|e^{i\lambda\varphi}\|_{A_p(\mathbb T^m)}$ as
$|\lambda|\rightarrow \infty, ~\lambda\in\mathbb R,$ for $C^1$ -smooth real
functions $\varphi$ on $\mathbb T^m$ (the one-dimensional case was investigated
by the author earlier). The lower estimates that we obtain have direct
analogues for the spaces $A_p(\mathbb R^m)$

### On the Fourier transform of the characteristic functions of domains with $C^1$ -smooth boundary

We consider domains $D\subseteq\mathbb R^n$ with $C^1$ -smooth boundary and
study the following question: when the Fourier transform $\hat{1_D}$ of the
characteristic function $1_D$ belongs to $L^p(\mathbb R^n)$?Comment: added two references; added footnotes on pages 6 and 1

### Directed Polymer -- Directed Percolation Transition

We study the relation between the directed polymer and the directed
percolation models, for the case of a disordered energy landscape where the
energies are taken from bimodal distribution. We find that at the critical
concentration of the directed percolation, the directed polymer undergoes a
transition from the directed polymer universality class to the directed
percolation universality class. We also find that directed percolation clusters
affect the characterisrics of the directed polymer below the critical
concentration.Comment: LaTeX 2e; 12 pages, 5 figures; in press, will be published in
Europhys. Let

### Classical and relativistic dynamics of supersolids: variational principle

We present a phenomenological Lagrangian and Poisson brackets for obtaining
nondissipative hydrodynamic theory of supersolids. A Lagrangian is constructed
on the basis of unification of the principles of non-equilibrium thermodynamics
and classical field theory. The Poisson brackets, governing the dynamics of
supersolids, are uniquely determined by the invariance requirement of the
kinematic part of the found Lagrangian. The generalization of Lagrangian is
discussed to include the dynamics of vortices. The obtained equations of motion
do not account for any dynamic symmetry associated with Galilean or Lorentz
invariance. They can be reduced to the original Andreev-Lifshitz equations if
to require Galilean invariance. We also present a relativistic-invariant
supersolid hydrodynamics, which might be useful in astrophysical applications.Comment: 22 pages, changed title and content, added reference

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