Related papers: A Floquet-Liapunov theorem in Frechet spaces
We obtain a Central Limit Theorem for closed Riemannian manifolds, clarifying along the way the geometric meaning of some of the hypotheses in Bhattacharya and Lin's Omnibus Central Limit Theorem for Fr\'echet means. We obtain our CLT…
We show that for infinite Tychonoff spaces X and Y the weak*-dual of Ck(X x Y) contains a basic sequence; moreover, the weak*-bidual of Ck(X) contains such a sequence as well. When X and Y are infinite compact spaces, we single out a…
In this paper we present some new results on the existence of solutions of generalized variational inequalities in real reflexive Banach spaces with Fr\'echet differentiable norms. Moreover, we also give some theorems about the structure of…
A continuous frame is a family of vectors in a Hilbert space which allows reproductions of arbitrary elements by continuous superpositions. Associated to a given continuous frame we construct certain Banach spaces. Many classical function…
We study systems on time scales that are generalizations of classical differential or difference equations. In this paper we consider linear systems and their small nonlinear perturbations. In terms of time scales and of eigenvalues of…
We prove a version of the variational Euler-Lagrange equations valid for functionals defined on Fr\'echet manifolds, such as the spaces of sections of differentiable vector bundles appearing in various physical theories.
Recently, versions of neural networks with infinite-dimensional affine operators inside the computational units (``neural operator'' networks) have been applied to learn solutions to differential equations. To enable practical computations,…
We show that norms on certain Banach spaces $X$ can be approximated uniformly, and with arbitrary precision, on bounded subsets of $X$ by $C^{\infty}$ smooth norms and polyhedral norms. In particular, we show that this holds for any…
For a grand canonical ensemble of classical point-like particles at equilibrium in continuous space we investigate the functional relationship between a stable and regular pair potential describing the interaction of the particles and the…
We systematically find conditions which yield locally uniform convergence in the Fourier inversion formula in one and higher dimensions. We apply the gained knowledge to the complex inversion formula of the Laplace transform to extend known…
We prove necessary conditions for Fredholmness of singular integral operators with piecewise continuous coefficients on weighted Banach function spaces. These conditions are formulated in terms of indices of submultiplicative functions…
Let $X$ be a Banach space. It is proved that an analogue of the Rubio de Francia square function estimate for partial sums of the Fourier series of $X$-valued functions holds true for all disjoint collections of subintervals of the set of…
In this work, we study the inverse problem of determining a potential coefficient in an abstract wave equation that includes a lower-order term. The equation incorporates a time-fractional derivative in the Caputo sense, as well as a…
We develop new approach for studying the abstract Cauchy problem $\dot{x}=Ax$, $x(0)=x_0\in D(A)$ for linear operators $A$ defined on a locally convex space $X$. This approach was firstly introduced in the paper "Chernoff and Trotter type…
In this paper, we show the new fixed point theorem in metric spaces. Furthermore, for this fixed point theorem, we apply to the Collatz conjecture.
A strong inspiration for studying perturbation theory for fractional evolution equations comes from the fact that they have proven to be useful tools in modeling many physical processes. In this paper, we study fractional evolution…
By methods of harmonic analysis, we identify large classes of Banach spaces invariant of periodic Fourier multipliers with symbols satisfying the classical Marcinkiewicz type conditions. Such classes include general (vector-valued) Banach…
We exhibit differential geometric structures that arise in numerical methods, based on the construction of Cauchy sequences, that are currently used to prove explicitly the existence of weak solutions to functional equations. We describe…
A fractional generalization of the Floquet theorem is suggested for fractional Schr\"odinger equations (FTSE)s with the time-dependent periodic Hamiltonians. The obtained result, called the fractional Floquet theorem (fFT), is formulated in…
We consider approximations of a continuous function on a countable normed Fr\'{e}chet space by analytic and $*$-analytic. Also we found a criterium of the existence of an extension of a continuous function from a dense subspace of a…