Related papers: Do law-invariant linear functionals collapse to th…

This work suggests using sampling theory to analyze the function space represented by neural networks. First, it shows, under the assumption of a finite input domain, which is the common case in training neural networks, that the function…

This paper proves that in Size Theory the comparison of multidimensional size functions can be reduced to the 1-dimensional case by a suitable change of variables. Indeed, we show that a foliation in half-planes can be given, such that the…

We introduce countably Markov interval functions and show that two inverse limits with countably Markov interval bonding functions are homeomorphic if the functions follow the same pattern. This result presents a generalization of…

We study the dynamic scaling hypothesis in invariant surface growth. We show that the existence of power-law scaling of the correlation functions (scale invariance) does not determine a unique dynamic scaling form of the correlation…

The behavior of certain weighted Hardy-type operators on rearrangement-invariant function spaces is thoroughly studied with emphasis being put on the optimality of the obtained results. First, the optimal rearrangement-invariant function…

We study a non linear regression model with functional data as inputs and scalar response. We propose a pointwise estimate of the regression function that maps a Hilbert space onto the real line by a local linear method. We provide the…

The work is devoted to the construction of a new type of intervals -- functional intervals. These intervals are built on the idea of expanding boundaries from numbers to functions. Functional intervals have shown themselves to be promising…

The functional linear model extends the notion of linear regression to the case where the response and covariates are iid elements of an infinite dimensional Hilbert space. The unknown to be estimated is a Hilbert-Schmidt operator, whose…

We study the covariant derivatives of an eigenfunction for the Laplace-Beltrami operator on a complete, connected Riemannian manifold with nonzero constant sectional curvature. We show that along every parallel tensor, the covariant…

The variation of spectral subspaces for linear self-adjoint operators under an additive bounded perturbation is considered. The objective is to estimate the norm of the difference of two spectral projections associated with isolated parts…

We consider multivariate splines and show that they have a random feature expansion as infinitely wide neural networks with one-hidden layer and a homogeneous activation function which is the power of the rectified linear unit. We show that…

The concept of b-linear functional and its different types of continuity in linear n-normed space are presented and some of their properties are being established. We derive the Uniform Boundedness Principle and Hahn-Banach extension…

For convex univalent functions we give instances where the sharp bound for various coefficient functionals are identical to those for the corresponding bound for the inverse function. We give instances where the sharp bounds differ and also…

Given a strictly positive measure, we characterize inner semicontinuous solid convex-valued mappings for which continuous functions which are selections almost everywhere are selections. This class contains continuous mappings as well as…

It is shown that any transverse invariant measure of a foliated space can be considered as a measure on the ambient space.

The Gleason-Kahane-\.Zelazko theorem states that a linear functional on a Banach algebra that is non-zero on invertible elements is necessarily a scalar multiple of a character. Recently this theorem has been extended to certain Banach…

A useful result is that if a bounded complex-valued path is Riemann-integrable, then its modulus is also Riemann-integrable. The extension of this last result to bounded paths taking values in a normed space is affirmed, as being true, in…

We show that a subspace $S$ of the space of real analytical functions on a manifold that satisfies certain regularity properties is contained in the set of solutions of a linear elliptic differential equation. The regularity properties are…

We characterize the rearrangement-invariant hull, with respect to a given measure $\mu$, of weighted Lebesgue spaces. The solution leads us to first consider when this space is contained in the sum of $(L^1 + L^\infty)(R, \mu)$ and the…

The collapse scenario of a scalar field along with a perfect fluid distribution is investigated for a conformally flat spacetime. The theorem for the integrability of an anharmonic oscillator has been utilized. For a pure power law…