Related papers: Weihrauch-completeness for layerwise computability

A classical theorem due to G.D. Birkhoff states that there exists an entire function whose translates approximate any given entire function, as accurately as desired, over any ball of the complex plane. We show this result may be…

We prove a polynomial bound in the "true complexity" problem of Gowers and Wolf. The proof uses only repeated applications of the Cauchy--Schwarz inequality, answering negatively a question posed by Gowers and Wolf. To choose and reason…

We study universal enveloping Hopf algebras of Lie algebras in the category of weakly complete vector spaces over the real and complex field.

We study an operator analogue of the classical problem of finding the rate of decay of an oscillatory integral on the real line. This particular problem arose in the analysis of oscillatory Riemann-Hilbert problems associated with partial…

Complexity theory can be viewed as the study of the relationship between computation and applications, understood the former as complexity classes and the latter as problems. Completeness results are clearly central to that view. Many…

We establish the Borg-Levinson theorem for elliptic operators of higher order with constant coefficients. The case of incomplete spectral data is also considered.

A logarithmic type Lieb-Thirring inequality for two-dimensional Schroedinger operators is established. The result is applied to prove spectral estimates on trapped modes in quantum layers.

We introduce a formal definition of Wolfram's notion of computational process based on cellular automata, a physics-like model of computation. There is a natural classification of these processes into decidable, intermediate and complete.…

Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider…

We classify the computability-theoretic complexity of two index sets of classes of first-order theories: We show that the property of being an $\aleph_0$-categorical theory is $\Pi^0_3$-complete; and the property of being an Ehrenfeucht…

We introduce an operator on problems in Weihrauch complexity, which we call the inverse limit, and which corresponds to an infinite compositional product. This operation arises naturally whenever one implements algorithms that produce a…

In the previous three papers in this series, [WKO1]-[WKO3] (arXiv:1405.1956, arXiv:1405.1955, and to appear), Z. Dancso and I studied a certain theory of "homomorphic expansions" of "w-knotted objects", a certain class of knotted objects in…

We obtain a generalized law of the iterated logarithm for a class of dependent processes with superdiffusive behaviour. Our results apply in particular to the Lorentz gas with infinite horizon.

We note that Weihrauch problems can be regarded as containers over the category of projective represented spaces and that Weihrauch reductions correspond exactly to container morphisms. We also show that Bauer's extended Weihrauch degrees…

Motivated by the work of Cappell, Deturck, Gluch and Miller, we extend the notion of cohomology of harmonic forms (of a compact manifold with boundary) to the abstract setting of Hilbert complexes. Then, we present some geometric…

This paper compares different representations (in the sense of computable analysis) of a number of function spaces that are of interest in analysis. In particular subspace representations inherited from a larger function space are compared…

We prove bilinear inequalities for differential operators in $\mathbb{R}^2$. Such type inequalities turned out to be useful for anisotropic embedding theorems for overdetermined systems and the limiting order summation exponent. However,…

We investigate the topological aspects of some algebraic computation models, in particular the BSS-model. Our results can be seen as bounds on how different BSS-computability and computability in the sense of computable analysis can be. The…

We study an extension of the Distributive Full Non-associative Lambek Calculus with iterative division operators. The iterative operators can be seen as representing iterative composition of linguistic resources or of actions. A complete…

For any class of operators which transform unary total functions in the set of natural numbers into functions of the same kind, we define what it means for a real function to be uniformly computable or conditionally computable with respect…