1,637 research outputs found
Harmonic analysis and the Riemann-Roch theorem
This paper is a continuation of papers: arXiv:0707.1766 [math.AG] and
arXiv:0912.1577 [math.AG]. Using the two-dimensional Poisson formulas from
these papers and two-dimensional adelic theory we obtain the Riemann-Roch
formula on a projective smooth algebraic surface over a finite field.Comment: 7 pages; to appear in Doklady Mathematic
Two types of Rubio de Francia operators on Triebel--Lizorkin and Besov spaces
We discuss generalizations of Rubio de Francia's inequality for
Triebel--Lizorkin and Besov spaces, continuing the research from [5]. Two
versions of Rubio de Francia's operator are discussed: it is shown that a
rotation factor is needed for the boundedness of the operator in some smooth
spaces while it is not essential in other spaces. We study the operators on
some "end" spaces of the Triebel--Lizorkin scale and then use usual
interpolation methods.Comment: 12 pages, 3 figure
Harmonic analysis on local fields and adelic spaces I
We develop a harmonic analysis on objects of some category of
infinite-dimensional filtered vector spaces over a finite field. It includes
two-dimensional local fields and adelic spaces of algebraic surfaces defined
over a finite field. The main result is the theory of the Fourier transform on
these objects and two-dimensional Poisson formulas.Comment: 69 pages; corrected typos and inserted some changes into the last
sectio
Interpretable collective intelligence of non-rational human agents
We outline how to create a mechanism that provides an optimal way to elicit,
from an arbitrary group of experts, the probability of the truth of an
arbitrary logical proposition together with collective information that has an
explicit form and interprets this probability. Namely, we provide strong
arguments for the possibility of the development of a self-resolving prediction
market with play money that incentivizes direct information exchange between
experts. Such a system could, in particular, motivate experts from all over the
world to collectively solve scientific or medical problems in a very efficient
manner. In our main considerations about real experts, they are not assumed to
be Bayesian and their behavior is described by utilities that satisfy the von
Neumann--Morgenstern axioms only locally.Comment: 41 pages, 4 figures, 3 table
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