Related papers: A remark on the approximation of plurisubharmonic …
We derive in this short article the non-asymptotical non-uniform sharp error estimation for the Bernstein's type approximation of continuous function based on the modern probabilistic apparatus.
Recently the authors have explored new concepts of plurisubharmonicity and pseudoconvexity, with much of the attendant analysis, in the context of calibrated manifolds. Here a much broader extension is made. This development covers a wide…
We study the approximation of functions which are invariant with respect to certain permutations of the input indices using flow maps of dynamical systems. Such invariant functions includes the much studied translation-invariant ones…
The goal of this work is to prove the regularity of certain quasi-plurisubharmonic upper envelopes. Such envelopes appear in a natural way in the construction of hermitian metrics with minimal singularities on a big line bundle over a…
This paper generalizes recent advances on quadratic manifold (QM) dimensionality reduction by developing kernel methods-based nonlinear-augmentation dimensionality reduction. QMs, and more generally feature map-based nonlinear corrections,…
Potential functional approximations are an intriguing alternative to density functional approximations. The potential functional that is dual to the Lieb density functional is defined and properties given. The relationship between…
The numerical evaluation of an individual Bessel or Hankel function of large order and large argument is a notoriously problematic issue in physics. Recurrence relations are inefficient when an individual function of high order and argument…
A ``self--similar'' example is constructed that shows that a conjecture of N. U. Arakelyan on the order of decrease of deficiencies of an entire function of finite order is not true.
We consider the pointwise approximation of a subharmonic function by the logarithm of the modulus of an entire function up to a bounded quantity. In the case of finite order an estimate from below of the planar Lebesgue measure of an…
We compute the motivic nearby cycles of functions obtained by composition with a polynomial which is non-degenerate with respect to its Newton polyhedron. Our result involves new convolution operators and generalized nearby cycles.
It is well-known that non-linear approximation has an advantage over linear schemes in the sense that it provides comparable approximation rates to those of the linear schemes, but to a larger class of approximands. This was established for…
We define two recursive functions obtained by decomposition of a given interval into four close parts and prove two lemmas which determine features of these functions.
In this paper we introduce, via a Phragmen-Lindel\"of type theorem, a maximal plurisubharmonic function in a strongly pseudoconvex domain. We call such a function the {\sl pluricomplex Poisson kernel} because it shares many properties with…
Building up on our previous works regarding $q$-deformed $P$-partitions, we introduce a new family of subalgebras for the ring of quasisymmetric functions. Each of these subalgebras admits as a basis a $q$-analogue to Gessel's fundamental…
Let $x \in \mathbb{R}$ be arbitrary and consider the `greedy' approximation of $x$ by signed harmonic sums: given $a_n = \sum_{k \leq n} \varepsilon_k/k$ with $\varepsilon_k \in \left\{-1,1\right\}$, we set $\varepsilon_{n+1} = 1$ if $a_n…
This work is concerned with the kernel-based approximation of a complex-valued function from data, where the frequency response function of a partial differential equation in the frequency domain is of particular interest. In this setting,…
We consider universal approximations of symmetric and anti-symmetric functions, which are important for applications in quantum physics, as well as other scientific and engineering computations. We give constructive approximations with…
A classical result of Carleman, based on the theory of quasianalytic functions, shows that polynomials are dense in $L^2(\mu)$ for any $\mu$ such that the moments $\int x^k d\mu$ do not grow too rapidly as $k \to \infty$. In this work, we…
In this paper, we present an explicit description for the boundary behavior of the Bergman kernel function, the Bergman metric, and the associated curvatures along certain sequences converging to an $h$-extendible boundary point.
The asymptotic analysis of Bergman kernels with respect to exponentially varying measures near emergent interfaces has attracted recent attention. Such interfaces typically occur when the associated limiting Bergman density function…