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- Sjödin, Tord, 1944-
(författare)
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A note on Gram-Schmidt's algorithm for a general angle
- 2009
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Ingår i: Normat. - Göteborg. - 0801-3500. ; 57:4, s. 173-179
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Tidskriftsartikel (refereegranskat)abstract
- Gram-Schmidts algoritm ger en parvis ortogonal mängd från en linjärt oberoende mängd i ett allmännt vektorrum med inre produkt. Vi ger en algoritm som konstruerar en mängd där vektorerna parvis har en godtycklig på förhand given vinkel, i alla fall där detta är möjligt.
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- Sjödin, Tord, 1944-
(författare)
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A Short and Unified Proof of Kummer's Test
- 2018
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- Kummer’s test from 1835 states that the positive series ∑∞n=1an is convergent if and only if there is a sequence {Bn}∞1 of positive numbers such that Bn·an/an+1−Bn+1 ≥ 1, for all sufficiently large n. We present an exact analysis and a short and unified proof of Kummer’s test. The test has been applied to differential equations and studied in mathematical philosophy.
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- Sjödin, Tord, 1944-
(författare)
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Continuous functions and Riesz type potentials in homogeneous spaces
- 2015
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Ingår i: Potential Analysis. - New York : Springer-Verlag New York. - 0926-2601 .- 1572-929X. ; 43:3, s. 495-511
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Tidskriftsartikel (refereegranskat)abstract
- We develop a potential theory for a Riesz type kernel in a homogeneous space and characterize the compact sets K with capacity zero as the sets K for which every continous function f on K is the restriction to K of a continuous potential Uσfk of an absolutely continuous measure σ f supported in an arbitrarily small neighbourhood of K. The measure σ f can be choosen as a suitable restriction of a single measure σ that only depends on the set K and the kernel k.
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| 6. |
- Sjödin, Tord, 1944-
(författare)
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Explaining Kummer's test
- 2015
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- Mathematical theorems and their proofs are often described as being beautyful, natural or explanatory. This paper treats the last case and discusses explanatory versus non explanatory proofs using a convergence theorem for positive series due to Kummer, called Kummer's test. This example was studied by Pringsheim already in the beginning in the last century and has recently been discussed by Hafner and Mancuso in relation to Steiner's criteria for an explanatory proof. We provide a mathematical analysis of Kummer's test and give a proof that we claim is explanatory in this sense. Besides this we answer a number of questions that are frequently asked about the test.
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- Sjödin, Tord, 1944-
(författare)
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Nonlinear potential theory in Lebesque spaces with mixed norm
- 1988
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Ingår i: Potential Theory, Prague, 1987. - New York : Plenum Publishing Corporation. - 0306428385 ; , s. 325-331
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Konferensbidrag (refereegranskat)abstract
- The classical potential theory for the Riesz kernel in the d-dimentional Euclidean space has been generalized in many different ways. We are here concerned with the L^p-potential theory which appeared around 1970 in papers by V.G. Maz'ya, V. P, Havin and N. G. Mayers. In this paper we extend that theory to the so called Lebesgue spaces with mixed norm.
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| 9. |
- Sjödin, Tord, 1944-
(författare)
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On Multivariate Hyperbolically Completely Monotone Densities and Their Laplace transforms
- 2015
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- We study classes of multivariate (bivariate) random variables with hyperbolically completely monotone densities (MVHCM) and prove that these classes are closed with respect to the Laplace transform. We then use this result to define new classes of bivariate generalized gamma convolutions (BVGGC_L) that contain Bondesson's class BVGGC in the strong sense.
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