Related papers: Nonlinear analysis with resurgent functions
The theory of resurgence uniquely associates a factorially divergent formal power series with a collection of exponentially small non-perturbative corrections paired with a set of complex numbers known as Stokes constants. When the Borel…
We develop a nonlinear theory for infrahyperfunctions (also referred to as quasianalytic (ultra)distributions by L. H\"{o}rmander). In the hyperfunction case our work can be summarized as follows. We construct a differential algebra that…
A reconstruction problem is formulated for Sperner systems, and infinite families of nonreconstructible Sperner systems are presented. This has an application to a reconstruction problem for functions of several arguments and identification…
We obtain recurrences for smallest parts functions which resemble Euler's recurrence for the ordinary partition function. The proofs involve the holomorphic projection of non-holomorphic modular forms of weight 2.
A method is presented for calculating solutions to differential equations analytically for a variety of problems in physics. An iteration procedure based on the recently proposed BLUES (Beyond Linear Use of Equation Superposition) function…
A differential algebra of nonlinear generalized functions is presented as a tool for a wide range of nonsmooth nonlinear problems. The power of the differential algebra is used to do mathematical calculations or proofs; then the final…
Many problems in nonlinear analysis and optimization, among them variational inequalities and minimization of convex functions, can be reduced to finding zeros (namely, roots) of set-valued operators. Hence numerous algorithms have been…
Colombeau algebras constitute a convenient framework for performing nonlinear operations like multiplication on Schwartz distributions. Many variants and modifications of these algebras exist for various applications. We present a…
We present numerical techniques based on generalized functions adapted to nonlinear calculations. They concern main numerical engineering problems ruled by-or issued from-nonlinear equations of continuum mechanics. The aim of this text is…
Motivated by partition regularity problems of homogeneous quadratic equations, we prove multiple recurrence and convergence results for multiplicative measure preserving actions with iterates given by rational sequences involving…
Connecting orbits are important invariant structures in the state space of nonlinear systems and various techniques are designed for their computation. However, a uniform analytic approximation of the whole orbit seems rare. Here, based on…
We develop a functional calculus for $d$-tuples of non-commuting elements in a Banach algebra. The functions we apply are free analytic functions, that is nc functions that are bounded on certain polynomial polyhedra.
We describe a numerical algorithm for evaluating the numbers of roots minus the number of poles contained in a region based on the argument principle with the function of interest being written as a Mellin transformation of a usually…
We present a formal analysis of nonlinear response functions in terms of correlation functions in real- and imaginary-time domains. In particular, we show that causal nonlinear response functions, expressed in terms of nested commutators in…
We discuss non commutative functions, which naturally arise when dealing with functions of more than one matrix variable.
We present in this paper the motivation and theory of nonlinear spectral representations, based on convex regularizing functionals. Some comparisons and analogies are drawn to the fields of signal processing, harmonic analysis and sparse…
We introduce constructive and classical systems for nonstandard arithmetic and show how variants of the functional interpretations due to Goedel and Shoenfield can be used to rewrite proofs performed in these systems into standard ones.…
In the multicentric calculus one takes a polynomial with simple roots as a new global variable and replaces scalar functions {\varphi} by functions f taking values in C^d with d the degree of the polynomial leading to an efficient…
We consider a class of $n^{\text{th}}$-order linear ordinary differential equations with a large parameter $u$. Analytic solutions of these equations can be described by (divergent) formal series in descending powers of $u$. We demonstrate…
In this paper, we study inverse boundary problems associated with semilinear parabolic systems in several scenarios where both the nonlinearities and the initial data can be unknown. We establish several simultaneous recovery results…