Related papers: Lefschetz operators on convex valuations

Classical integral representation of the Mellin type kernel in terms of the Laplace integral gives an idea to construct a new class of non-convolution (index) transforms. Particular examples give the Kontorovich-Lebedev-like transformation…

We show an analogue of the Klain-Schneider theorem for valuations that are invariant under rotations around a fixed axis, called zonal. Using this, we establish a new integral representation of zonal valuations involving mixed area measures…

Bilevel programming has recently received a great deal of attention due to its abundant applications in many areas. The optimal value function approach provides a useful reformulation of the bilevel problem, but its utility is often limited…

We discuss variants of construction of measurable subgradients for multivariate convex functions and the problem of characterization of the $\Delta_2$-condition in terms of their directional derivatives. Furthermore we study related basic…

We present an alternative way of solving the steerable kernel constraint that appears in the design of steerable equivariant convolutional neural networks. We find explicit real and complex bases which are ready to use, for different…

We study several fundamental operators in harmonic analysis related to Bessel operators, including maximal operators related to heat and Poisson semigroups, Littlewood-Paley-Stein square functions, multipliers of Laplace transform type and…

We define graded hyper-algebras of vector-valued Siegel modular forms, which allow us to study tensor products of the latter. We also define vector-valued Hecke operators for Siegel modular forms at all places of ${\mathbb Q}$, acting on…

In this work we establish a Stokes-type integral equality for scalarly essentially integrable forms on an orientable smooth manifold with values in the locally convex linear space $\langle B(G),\sigma(B(G),\mathcal{N})\rangle$, where $G$ is…

We introduce a class of (tuples of commuting) unbounded operators on a Banach space, admitting smooth functional calculi, that contains all operators of Helffer-Sj\"ostrand type and is closed under the action of smooth proper mappings.…

For $(n-2)$ free divisor classes on a smooth projective variety of dimension $n$, the product of these free divisor classes induces a Lefschetz type operator acting on the N\'{e}ron-Severi space or the cohomology group of $(1,1)$ classes.…

We provide transformation matrices for arbitrary Lorentz transformations of multidimensional Hermite functions in any dimension. These serve as a valuable tool for analyzing spacetime properties of MHS fields, and aid in the description of…

A classification of all continuous GL(n) equivariant Minkowski valuations on convex bodies in $\mathbb{R}^n$ is established. Together with recent results of F.E. Schuster and the author, this article therefore completes the description of…

In this paper we study differential operators of the form \begin{align*} \left[\mathcal{L}_\infty v \right](x) = A\triangle v(x) + \left\langle Sx,\nabla v(x) \right\rangle - Bv(x), \,x \in \mathbb{R}^d, \,d \geqslant 2, \end{align*} for…

New index transforms, involving squares of Kelvin functions, are investigated. Mapping properties and inversion formulas are established for these transforms in Lebesgue spaces. The results are applied to solve a boundary value problem on…

An invex function generalizes a convex function in the sense that every stationary point is a global minimizer. Recently, invex functions and their subclasses have attracted attention in signal processing and machine learning. However,…

We investigate the weighted $L_p$ affine surface areas which appear in the recently established $L_p$ Steiner formula of the $L_p$ Brunn Minkowski theory. We show that they are valuations on the set of convex bodies and prove isoperimetric…

Functions satisfying the functional equation \begin{align*} \sum_{r=0}^{n-1} (-1)^r f(x+ry, ny) = f(x,y), \quad \text{for any positive odd integer $n$}, \end{align*} are named the alternating invariant functions. Examples of such functions…

We introduce a new concept of the so-called {\it composite wavelet transforms}. These transforms are generated by two components, namely, a kernel function and a wavelet function (or a measure). The composite wavelet transforms and the…

We develop a general theory of multilinear singular integrals with operator-valued kernels, acting on tuples of UMD Banach spaces. This, in particular, involves investigating multilinear variants of the $\mathcal R$-boundedness condition…

We prove a Positivstellensatz for operator-valued noncommutative polynomials that are positive on matrix convex sets. Specifically, let $p$ be an operator-valued polynomial in $B(H)\otimes C<x>$ of degree at most $2d+1$, where $H$ is…