Christer Kiselman | Uppsala University (original) (raw)

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Papers by Christer Kiselman

This essay describes orbits of particles passing near the sun, first according to Newton's celest... more This essay describes orbits of particles passing near the sun, first according to Newton's celestial mechanics and then according to Einstein's general theory of relativity. Attempts to verify the latter by observing the deflection of light during total solar eclipses are mentioned. Confirmation also comes from measurements of the delay in the arrival of reflected light, as well as from the use of Very Long Baseline Interferometry (VLBI). A comparison of explanations of these phenomena reveals contradicting statements.

WORLD SCIENTIFIC eBooks, Dec 5, 2016

Müntz and Szász, the condition En-' .' =is necessary and sufficient in order that polynomials in ... more Müntz and Szász, the condition En-' .' =is necessary and sufficient in order that polynomials in the powers x"' and 1 suffice to approximate uniformly an arbitrary continuous function in the interval 0 < x < 1, i .e ., that these powers span the space C of continuous functions in that interval. If the series converges, these powers, then, will span a certain closed linear proper sub-manifold ill of the space C. It is clear from the Müntz-Szász result that if M' and M" are two such manifolds, then their union M' + M" cannot span the space C either, although the latter is quite possible in general for two proper closed linear sub-manifolds. Such a manifold M is then in a dimensional sense "small", and it is not unreasonable to conjecture that the functions comprising 11 are subject to quite restrictive conditions. We shall show, in fact, that every such function may be extended to be analytic in the interior of the unit circle. The power series for this function contains only powers x", and it may diverge at the point x = 1. It will converge at that point, however, if the sequence {n ; } is lacunary (n ; ;., n i > c > 1) .

Elementa, 1993

Recension av: Fractals, for the Classroom: Strategic Activities Volume One : av Heinz-Otto Peitge... more Recension av: Fractals, for the Classroom: Strategic Activities Volume One : av Heinz-Otto Peitgen, Harmut Jurgens, Dietmar Saupe, Evan Maletsky, Terry Perciante, Lee Yunker

Complex Variables and Elliptic Equations, Feb 16, 2022

Ramon Edgar Moore and Alexander M. Gofen introduced a generalization of Joseph Liouville's concep... more Ramon Edgar Moore and Alexander M. Gofen introduced a generalization of Joseph Liouville's concept of elementary functions. Gofen even defined two variants of these, viz. scalar generalized elementary functions and vector generalized elementary functions, and formulated a conjecture concerning them. We prove that, for some modified conjectures, the two classes are different.

Chapman and Hall/CRC eBooks, Feb 1, 2022

Dagstuhl Reports, 2019

In computer vision, geometric processing and image analysis, the notation of a shape of a 3-D obj... more In computer vision, geometric processing and image analysis, the notation of a shape of a 3-D object has been studied either by an embedded manifold for the continuous stetting or as a collection of a discrete set of marker positions on the manifold. Within the last years, there have been many rapid developments in the field of shape representation, shape correspondence and shape manipulation with technical applications ranging from laser-range scanners to 3-D printing. Classic shape analysis tools from differential geometry have a fresh influence in the field, often powered by modern methods from optimization and numerical computing. At the same time, discrete geometric methods and related techniques such as from mathematical morphology have evolved significantly. Moreover, techniques like deep learning gained a significant influence in the development of corresponding methods and tools. New developments from tropical geometry have a high potential for use in shape analysis. The topics in our seminar addressed the sketched challenges and developments that will be useful for shape analysis. Especially we aimed to discuss the possibilities of combining fields like tropical geometry with more classical techniques as for instance from mathematical morphology. We discussed possibilities of applying machine learning methods in this context and considered recent advances from more classical fields like differential geometry and partial differential equations that can be useful for setting up and understanding shape analysis methods in all of these approaches. This seminar brought together 26 researchers from North America and Europe engaged in recent and upcoming developments in shape analysis who view these challenges from different perspectives and who together discussed the pressing open problems and novel solutions to them.

Mathematica Scandinavica, Jun 1, 1968

Mathematica Scandinavica, Dec 1, 1987

Arkiv för Matematik, Aug 1, 1966

Bulletin de la Société Mathématique de France, 1969

Prolongement des solutions d'une équation aux dérivées partielles à coefficients constants Bullet... more Prolongement des solutions d'une équation aux dérivées partielles à coefficients constants Bulletin de la S. M. F., tome 97 (1969), p. 329-356 <http://www.numdam.org/item?id=BSMF_1969__97__329_0> © Bulletin de la S. M. F., 1969, tous droits réservés. L'accès aux archives de la revue « Bulletin de la S. M. F. » (http: //smf.emath.fr/Publications/Bulletin/Presentation.html) implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/ conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/

Springer eBooks, Nov 24, 2006