Related papers: Constructing $\omega$-free Hardy fields
K. Harada conjectured for any finite group $G$, the product of sizes of all conjugacy classes is divisible by the product of degrees of all irreducible characters. We study this conjecture when $G$ is the general linear group over a finite…
The Polchinski exact renormalization group equation for a scalar field theory in arbitrary dimensions is translated, by means of a covariant Hamiltonian formalism, into a partial differential equation for an effective Hamiltonian density…
It is shown how to construct a time-independent Hamiltonian having only one degree of freedom from which an arbitrary linear constant-coefficient evolution equation of any order can be derived.
Let P be a linear, second order, elliptic operator satisfying a Hardy inequality with potential W (i.e. $P-W\geq0$) and best constant $\alpha$. We give conditions so that the spectrum of $W^{-1}P$ is $[\alpha,\infty)$. We apply this to…
We prove a one-dimensional Hardy inequality on the halfline with sharp constant, which improves the classical form of this inequality. As a consequence of this new inequality we can rederive known doubly weighted Hardy inequalities. Our…
The Hodge equations for 1-forms are studied on Beltrami's projective disc model for hyperbolic space. Ideal points lying beyond projective infinity arise naturally in both the geometric and analytic arguments. An existence theorem for…
We provide a construction of binary pseudorandom sequences based on Hardy fields $\mathcal{H}$ as considered by Boshernitzan. In particular we give upper bounds for the well distribution measure and the correlation measure defined by…
In this paper we investigate the possible supersymmetric extensions for the massive (bi)gravity theories in the lowest non-trivial order. For this purpose we construct the cubic interaction vertices for massive spin-2 and one or two massive…
In the setting of spaces of homogeneous type, we give a direct proof of the local Tb theorem for singular integral operators. Motivated by questions of S. Hofmann, we extend it to the case when the integrability conditions are lower than 2,…
We prove a sharp $L^p$ weighted Hardy inequality involving boundary distance $\delta$ for any domain $\Omega\subsetneq \mathbb R^n$. The inequality may be improved substantially under the additional assumption that $-\log \delta$ is…
We show that every valued differential field has an immediate strict extension that is spherically complete. We also discuss the issue of uniqueness up to isomorphism of such an extension.
For Baouendi-Grushin vector fields, we prove Hardy, Hardy-Rellich, and Rellich identities and inequalities with sharp constants. Our explicit remainder terms significantly improve than those found in the literature. Our arguments are built…
Esnault asked whether every smooth complex projective variety with infinite fundamental group has a nonzero symmetric differential (a section of a symmetric power of the cotangent bundle). In a sense, this would mean that every variety with…
We take advantage of the superspace formalism and explicitly find the N=2 supersymmetric extension of the Maxwell Chern-Simons model. In our construction a special form of a potential term and indispensability of an additional neutral…
We build on the results of [6] to show that the homology groups $\mathrm{H}_{r_1+r_2}(Y_0(\mathcal{N}_\Sigma),\mathcal{O})_{\mathfrak{m}_\Sigma}$ of arithmetic manifolds are free over certain deformation rings $R_\Sigma$, when there are…
We present a new multisymplectic framework for second-order classical field theories which is based on an extension of the unified Lagrangian-Hamiltonian formalism to these kinds of systems. This model provides a straightforward and simple…
Varieties without deformations are defined over a number field. Several old and new examples of this phenomenon are discussed such as Bely\u \i\ curves and Shimura varieties. Rigidity is related to maximal Higgs fields which come from…
We establish the first extension results for divergence-free (or solenoidal) elements of $\mathrm{L}^{1}$-based function spaces. Here, the key point is to preserve the solenoidality constraint while simultaneously keeping the underlying…
Electrostatic bender optics are derived up to second order (third order in fields and the Hamiltonian) and applied to the proposed EDM proton ring. The results for linear optics agree with those already presented by V.\ Lebedev (Nov.\ 18,…
We consider an Abelian gauge field coupled to a particular truncation of Horndeski theory. The Galileon field has translation symmetry and couples non minimally both to the metric and the gauge field. When the gauge-scalar coupling is zero…