Related papers: Dot product invariant valuations on Lip$(S^{n-1})$
Using Maz'ya type integral identities with power weights, we obtain new boundary estimates for biharmonic functions on Lipschitz and convex domains in $R^n$. For $n\ge 8$, combined with a result in \cite{S2}, these estimates lead to the…
We find an explicit general formula for the iterated local monodromy of singularities of the Hadamard product of functions with integrable singularities. The formula implies the invariance by Hadamard product of the class of functions with…
We consider the Poisson algebra S(M) of smooth functions on T^*M which are fiberwise polynomial. In the case where M is locally projectively (resp. conformally) flat, we seek the star-products on S(M) which are SL(n+1,R) (resp.…
We study the space of invariant generalized functions supported on an orbit of the action of a real algebraic group on a real algebraic manifold. This space is equipped with the Bruhat filtration. We study the generating function of the…
It is proved the existence of single-valued analytic solutions in the unit disk and multivalent analytic solutions in domains bounded by a finite collection of circles for the Riemann-Hilbert problem with coefficients of sigma-finite…
Recently, Hairer et. al (2012) showed that there exist SDEs with infinitely often differentiable and globally bounded coefficient functions whose solutions fail to be locally Lipschitz continuous in the strong L^p-sense with respect to the…
The aim of this paper is twofold. First, we establish the representation formula and the uniqueness of the solutions to a class of inhomogeneous biharmonic Dirichlet problems, and then prove the bi-Lipschitz continuity of the solutions.
Let $D$ be a bounded domain in the complex plane with Lipschitz boundary. In the paper, we construct an integral solution operator $T[f]$ for any $\overline{\partial}$ closed $(0,1)$-form $f\in L^p_{(0,1)}(D^n)$ solving the Cauchy-Riemain…
We study a method for calculating the utility function from a candidate of a demand function that is not differentiable, but is locally Lipschitz. Using this method, we obtain two new necessary and sufficient conditions for a candidate of a…
We obtain a necessary and sufficient condition for embeddings of integral Lipschitz classes Lip(\alpha; p) into classes \Lambda BV of functions of bounded \Lambda-variation.
Classifications of $\rm{SL}(n)$ covariant function-valued valuations are established with some assumptions of continuity. New valuations, for example, weighted moment functions, are introduced and our classifications give unified…
We consider the bounded linear operators with domain in the Hilbert space $L^2(S^n)$, $n=2,3,5$ and describe its symbolic calculus defined by the Berezin quantization. In particular, we derive an explicit formula for the composition of…
We consider a functional calculus for compact operators, acting on the singular values rather than the spectrum, which appears frequently in applied mathematics. Necessary and sufficient conditions for this singular value functional…
In this paper we investigate the nature of stationary points of functionals on the space of Riemannian metrics on a smooth compact manifold. Special cases are spectral invariants associated with Laplace or Dirac operators such as functional…
We estimate the second order linking invariants of Lipschitz maps from an n-dimensional ellipse. The estimate uses a new directionally-dependent version of the isoperimetric inequality for cycles inside the ellipse. Using this work, we…
We study Seifert linking form which is an invariant of embeddings of punctured $n$-manifolds in $\mathbb R^{2n-1}$. For punctured $n$-manifold $N_0$ the values of this invariant are integer valued bilinear symmetric forms on…
Recently, Gekeler proved that the group of invertible analytic functions modulo constant functions on Drinfeld's upper half space is isomorphic to the dual of an integral generalized Steinberg representation. In this note we show that the…
We obtain a family of strict $\hat G$-invariant products on the space of holomorphic functions on a semisimple coadjoint orbit of a complex connected semisimple Lie group $\hat G$. By restriction, we also obtain strict $G$-invariant…
One of the goals of this article is to define a an unified setting adapted to the description of means (normalized integrals or invariant means) on an infinite product of measured spaces with infinite measure. We first remark that some…
We study the well-posedness and the long-time behavior of almost periodic solutions to stochastic degenerate parabolic-hyperbolic equations in any space dimension, under the assumption of Lipschitz continuity of the flux and viscosity…