Related papers: Isotropic functions revisited

We introduce a new class $\mathcal{FV}(\Omega,E)$ of spaces of weighted functions on a set $\Omega$ with values in a locally convex Hausdorff space $E$ which covers many classical spaces of vector-valued functions like continuous, smooth,…

In this paper, we give a complete classification of critical metrics of the volume functional on a compact manifold $M$ with boundary $\partial M$ having positive isotropic curvature. We prove that for a pair $(f, \kappa)$ of a nontrivial…

Let F be a p-adic field and let G be a connected reductive group defined over F. We assume p is big. Denote g the Lie algebra of G. We normalize suitably a Fourier-transform on the space of smooth functions with compact support on g(F),…

We are interested in the $L^2$-holomorphic automorphic functions on a $g$-dimensional complex space $V^g_{\mathbb{C}}$ endowed with a positive definite hermitian form and associated to isotropic discrete subgroups $\Gamma$ of rank $2\leq r…

Let $\mathbb{F}_q$ be a finite field with $q$ elements, $n\geq2$ a positive integer, $\mathbb{V}_0$ a $n$-dimensional vector space over $\mathbb{F}_q$ and $\mathbb{T}_0$ the set of all linear functionals from $\mathbb{V}_0$ to…

Let $V$ be a vertex operator superalgebra and $g=\left(1\ 2\ \cdots k\right)$ be a $k$-cycle which is viewed as an automorphism of the tensor product vertex operator superalgebra $V^{\otimes k}$. In this paper, we construct an explicit…

Let $V$ be a vector space over a field $\mathbb F$ with scalar product given by a nondegenerate sesquilinear form whose matrix is diagonal in some basis. If $\mathbb F=\mathbb C$, then we give canonical matrices of isometric and selfadjoint…

We prove a local version of a recently established theorem by Myroshnychenko, Ryabogin and the second named author. More specifically, we show that if $n\geq 3$, $g:\mathbb{S}^{n-1}\to\mathbb{R}$ is an even bounded measurable function, $U$…

Suppose that $F$ is a smooth and connected complex surface (not necessarily compact) containing a smooth rational curve with positive self-intersection. We prove that if there exists a non-constant meromorphic function on $F$, then the…

We show that for every connected analytic subvariety $V$ there is a pseudoconvex set $\Omega$ such that every bounded matrix-valued holomorphic function on $V$ extends isometrically to $\Omega$. We prove that if $V$ is two analytic disks…

Let $F$ be a $p$-adic field and let $G$ be a connected reductive group defined over $F$. We assume $p$ is big. Denote $\mathfrak{g}$ the Lie algebra of $G$. To each vertex $s$ of the reduced Bruhat-Tits' building of $G$, we associate as…

In this note, we continue to highlight some applications of Theorem 1 of [3]. Here is a sample: Let $X$ be an open set in ${\bf C}^n$, $\Omega$ an open convex set in ${\bf C}$ and $f, g : X\to {\bf C}$ two holomorphic functions such that…

Let G be the group of points of a quasi-split reductive algebraic group over a local field F. It follows from the local Langlands conjectures that to every non-trivial additive character of F and every representation of the Langlands dual…

A topological space $A$ is said to be compatible with a set $\Sigma$ of equations (involving operation symbols $F_t$) iff there are continuous operations $\overline F_t$ identically satisfying $\Sigma$ on $A$. The paper's main focus is on…

We study equivalence relations that arise from translation actions $\Gamma\curvearrowright G$ which are associated to dense embeddings $\Gamma<G$ of countable groups into second countable locally compact groups. Assuming that $G$ is simply…

Let $\varphi $ be a negative plurisubharmonic function in a pseudoconvex domain $\Omega$ in $\mathbb{C}^{n}$ and $f$ be a bounded holomorphic function belonging to $L^{2}(\Omega, \varphi)$. For all negative plurisubharmonic functions $\psi$…

Isotropic functions of positions $\hat{\bf r}_1, \hat{\bf r}_2,\ldots, \hat{\bf r}_N$, i.e. functions invariant under simultaneous rotations of all the coordinates, are conveniently formed using spherical harmonics and Clebsch-Gordan…

Let $\Gamma$ be a co-compact Fuchsian group of isometries on the Poincar\'e disk $\DD$ and $\Delta$ the corresponding hyperbolic Laplace operator. Any smooth eigenfunction $f$ of $\Delta$, equivariant by $\Gamma$ with real eigenvalue…

Let $M$ be a compact smooth manifold with corners and $N$ be a finite dimensional smooth manifold without boundary which admits local addition. We define a smooth manifold structure to general sets of continuous mapings $\mathcal{F}(M,N)$…

We establish the existence of a regular functional $M$-position, in the sense of Pisier, for geometric log-concave functions. This provides a functional analogue of Pisier's regular $M$-positions for convex bodies and yields uniform control…