相关论文: On geometric characterizations of mappings generat…
We study numerical approaches to computation of spectral properties of composition operators. We provide a characterization of Koopman Modes in Banach spaces using Generalized Laplace Analysis. We cast the Dynamic Mode-Decomposition type…
We solve the following problem: to describe in geometric terms all differential operators of the second order with a given principal symbol. Initially the operators act on scalar functions. Operator pencils acting on densities of arbitrary…
This paper intends to lay the theoretical foundation for the method of functional maps, first presented in 2012 by Ovsjanikov, Ben-Chen, Solomon, Butscher and Guibas in the field of the theory and numerics of maps between shapes. We show…
In this note we revisit a result in [9], where we established nonlocal isoperimetric inequalities and the related embeddings for Besov spaces adapted to a class of H\"ormander operators of Kolmogorov-type. We provide here a new proof which…
We recall the notion of a differential operator over a smooth map (in linear and non-linear settings) and consider its versions such as formal $\hbar$-differential operators over a map. We study constructions and examples of such operators,…
We prove that any linear operator with kernel in a Gelfand-Shilov space is a composition of two operators with kernels in the same Gelfand-Shilov space. We also give links on numerical approximations for such compositions. We apply these…
Let $B_{n}$ be the unit ball in the complex vector space $\mathbb{C}^{n}$, and let $\varphi: B_{n}\rightarrow B_{n}$ be a holomorphic mapping. In this paper, we characterize those symbols $\varphi$ such that composition operators…
In a doubling metric measure space $(X,\rho,\mu)$ supporting a Poincar\'e inequality, we give a new characterisation of first-order Sobolev spaces by mean oscillations, and extend previous characterisations of constant functions in terms of…
In this paper, we investigate the boundedness of composition operators defined on a quasi-Banach space continuously included in the space of smooth functions on a manifold. We prove that the boundedness of a composition operator strongly…
In this paper, we give new characterizations of monopole bundle systems of complex hypermanifolds in $n$-dimensional spaces for certain classes of operators. In particular, we consider the reproducing kernels for decomposable polynomials of…
We reformulate superalgebra and supergeometry in completely categorical terms by a consequent use of the functor of points. The increased abstraction of this approach is rewarded by a number of great advantages. First, we show that one can…
In this paper, we prove the uniform estimates for the resolvent $(\Delta - \alpha)^{-1}$ as a map from $L^q$ to $L^{q'}$ on real hyperbolic space $\mathbb{H}^n$ where $\alpha \in \mathbb{C}\setminus [(n - 1)^2/4, \infty)$ and $2n/(n + 2)…
In this paper we characterize essential norm of composition operators on the spaces of Harmonic Bloch functions. These results extends the similar results that were proven for composition operators on Bloch spaces.
In this paper we consider composition operator $C_{\varphi} generated by nonsingular measurable transformation $T$ and multiplication operator $M_u$ generated by measurable function $u$ between two different Orlicz spaces, then we…
The aim of this article is to detect the ascent and descent of weighted composition operators on Lorentz spaces. We investigate the conditions on the measurable transformation $T$ and the complex-valued measurable function $u$ defined on…
We prove that any linear operator with kernel in a Pilipovi\'c or Gelfand-Shilov space can be factorized by two operators in the same class. We also give links on numerical approximations for such compositions. We apply these composition…
We give a characterization of metric space valued Sobolev maps in terms of weak* derivatives. This corrects a previous result by Haj{\l}asz and Tyson.
We extend Federer's coarea formula to mappings $f$ belonging to the Sobolev class $W^{1,p}(R^n;R^m)$, $1 \le m < n$, $p>m$, and more generally, to mappings with gradient in the Lorentz space $L^{m,1}(R^n)$. This is accomplished by showing…
We establish two types of characterizations for high order anisotropic Sobolev spaces. In particular, we prove high order anisotropic versions of Bourgain-Brezis- Mironescu's formula and Nguyen's formula.
We determine the boundedness and compactness of a large class of operators, mapping from general Banach spaces of holomorphic functions into a particular type of spaces of functions determined by the growth of the functions, or the growth…