相关论文: Analytic cell decomposition and analytic motivic i…

These are notes of a series of talks about motivic integration I gave on the M\"unster Model Theory Month. Readers are assumed to have some basic knowledge of model theory and of valued fields. The notes are closest to the Cluckers-Loeser…

This work is concerned with the convex analysis of functions defined on (not necessarily finite-dimensional) Hilbert spaces whose values depend solely on a certain ``spectrum'' of the arguments, a class we term ``spectral functions.'' We…

We develop an extension theory for analytic valuation rings in order to establish Ax-Kochen-Ersov type results for these structures. New is that we can add in salient cases lifts of the residue field and the value group and show that the…

Using Zeilberger generating function formula for the values of a discrete analytic function in a quadrant we make connections with the theory of structured reproducing kernel spaces, structured matrices and a generalized moment problem. An…

In a previous paper [1] it was discussed the viability of functional analysis using as a basis a couple of generic functions, and hence vectorial decomposition. Here we complete the paradigm exploiting one of the analysis methodologies…

Alesker's theory of generalized valuations unifies smooth measures and constructible functions on real analytic manifolds, extending classical operations on functions and measures. Alesker showed that these operations agree with the…

Functional ANOVA offers a principled framework for interpretability by decomposing a model's prediction into main effects and higher-order interactions. For independent features, this decomposition is well-defined, strongly linked with SHAP…

This work brings Mellin transforms into the realm of motivic integration. The new, larger class of motivic functions is stable under motivic Mellin and Fourier transforms, with general Fubini results and change of variables formulas. It…

A method for construction of analytic function f of the annihilation operator is given for the first time. f(z) is analytic on some compact domain that does not separate the complex plane. A new form of the identity is given, which is well…

Regarding quaternions as normal matrices, we first characterize the $2\times 2$ matrix-valued functions, defined on subsets of quaternions, whose values are quaternions. Then we investigate the regularity of quaternionic-valued functions,…

We discuss the deep relationship between $\infty$-categorical functional analysis and the anticipated theory of $p$-adic motives. The motivation fundamentally comes from applications essentially in arithmetics from very broad perspectives.…

We introduce spaces of exponential constructible functions in the motivic setting for which we construct direct image functors in the absolute and relative cases. This allows us to define a motivic Fourier transformation for which we get…

Fix a base field F, a finite field K and consider a sequence of central simple F-algebras A_1,...,A_n. In this note we provide some results toward a classification of the indecomposable motives lying in the motivic decompositions of…

In arXiv:1408.4708, Xu defines the dlt motivic zeta function associated to a regular function $f$ on a smooth variety $X$ over a field of characteristic zero. This is an adaptation of the classical motivic zeta function that was introduced…

Composition operators with analytic symbols on some reproducing kernel Hilbert spaces of entire functions on a complex Hilbert space are studied. The questions of their boundedness, seminormality and positivity are investigated. It is…

We introduce new and robust decompositions of mean-field Hartree-Fock (HF) and Kohn-Sham density functional theory (KS-DFT) relying on the use of localized molecular orbitals and physically sound charge population protocols. The new…

Certain integrable models are described by pairs (X,Y) of ADET Dynkin diagrams. At high energy these models are expected to have a conformally invariant limit. The S-matrix of the model determines algebraic equations, whose solutions are…

The analytic implicit function theorem is extended. The function f of the theorem is integrated with respect to the dependent variable of the implicit function. A geometrical interpretation is given for the sub-geometry of the integral…

We develop integration theory for integrating functions taking values into a Dedekind complete unital $f$-algebra $\mathbb{L}$ with respect to $\mathbb{L}$-valued measures. We then discuss and prove completeness results of…

This dissertation reports some first steps towards a compositional account of active inference and the Bayesian brain. Specifically, we use the tools of contemporary applied category theory to supply functorial semantics for approximate…