Related papers: Banach Manifold Structure and Infinite-Dimensional…
In this note, we show that if a Banach space X has a predual, then every bounded linear operator on X with a continuous functional calculus admits a bounded Borel functional calculus. A consequence of this is that on such a Banach space,…
We study an infinite system of ordinary differential equations that models the evolution of coagulating and fragmenting clusters, which we assume to be composed of identical units. Under very mild assumptions on the coefficients we prove…
Problem for the first order differential equation with an unbounded operator coefficient in Banach space and integral nonlocal condition is considered. An exponentially convergent algorithm is proposed and justified for the numerical…
The classical tools which ensure the completeness of vector fields and second order differential equations for mechanical systems are revisited. Possible extensions in three directions are discussed: infinite dimensional Banach and Hilbert…
An exponentially convergent numerical method for solving a differential equation with a right-hand fractional Riemann-Liouville time-derivative and an unbounded operator coefficient in Banach space is proposed and analysed for a…
Sufficient conditions for the invariance of evolution problems governed by perturbations of (possibly nonlinear) $m$-accretive operators are provided. The conditions for the invariance with respect to sublevel sets of a constraint…
This note aims to highlight the link between representable functionals and derivations on a Banach quasi *-algebra, i.e. a mathematical structure that can be seen as the completion of a normed *-algebra in the case the multiplication is…
The abstract Cauchy problem for the distributed order fractional evolution equation in the Caputo and in the Riemann-Liouville sense is studied for operators generating a strongly continuous one-parameter semigroup on a Banach space.…
We survey methods and results of fractional differential equations in which an unknown function is under the operation of integration and/or differentiation of fractional order. As an illustrative example, we review results on fractional…
The finite section method is a classical scheme to approximate the solution of an infinite system of linear equations. We present quantitative estimates for the rate of the convergence of the finite section method on weighted $\ell…
We prove, using a fixed point theorem in a Banach algebra, an existence result for a fractional functional differential equation in the Riemann-Liouville sense. Dependence of solutions with respect to initial data and an uniqueness result…
In the theory of causal fermion systems, the physical equations are obtained as the Euler-Lagrange equations of a causal variational principle. Studying families of critical measures of causal variational principles, a class of conserved…
The L-fractional derivative is defined as a certain normalization of the well-known Caputo derivative, so alternative properties hold: smoothness and finite slope at the origin for the solution, velocity units for the vector field, and a…
When a spatial process is recorded over time and the observation at a given time instant is viewed as a point in a function space, the result is a time series taking values in a Banach space. To study the spatio-temporal extremal dynamics…
It is proven that the kernel of the fermionic projector of regularized Dirac sea vacua in Minkowski Space is $L^4$-integrable. The proof is carried out in the specific setting of a continuous exponentially-decaying cutoff in momentum space.…
In this paper, we use a Banach fixed point theorem to obtain suficient conditions satisfying the convergence and exponential convergence of solutions for the linear system of advanced differential equations. The considered system with…
We investigate the conditional distributions of two Banach space valued, jointly Gaussian random variables. In particular, we show that these conditional distributions are again Gaussian and that their means and covariances can be…
We propose a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal…
Causal fermion systems are introduced as a general mathematical framework for formulating relativistic quantum theory. By specializing, we recover earlier notions like fermion systems in discrete space-time, the fermionic projector and…
The dynamics of spinorial wave functions in a causal fermion system is studied. A so-called dynamical wave equation is derived. Its solutions form a Hilbert space, whose scalar product is represented by a conserved surface layer integral.…