| 1. |
- Bernhardsson, Bo, et al.
(författare)
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Quaternary binary trilinear forms of norm unity
- 2006
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Ingår i: Proceedings of the Estonian Academy of Sciences. Physics & Mathematics. - 1406-0086. ; 55:3, s. 150-158
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Tidskriftsartikel (refereegranskat)
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| 2. |
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| 3. |
- Bernhardsson, Bo, et al.
(författare)
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Singular Values of Trilinear Forms
- 2001
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Ingår i: Experimental Mathematics. - : Informa UK Limited. - 1944-950X .- 1058-6458. ; 10:4, s. 509-518
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Tidskriftsartikel (refereegranskat)abstract
- Let T : H 1 × H 2 × H 3 → C be a trilinear form, where H 1, H 2, H 3 are separable Hilbert spaces. In the hypothesis that at least two of the three spaces are finite dimensional we show that the norm square λ = ∥T∥2 is a root of a certain algebraic equation, usually of very high degree, which we baptize the millennia] equation, because it is an analogue of the secular equation in the bilinear case. More generally, as indicated in the title, we can consider singular values of a trilinear form and their squares too satisfy the same equation. We work out the binary case (all three spacesare two dimensional). Even in this case the situation is complex, so, in the absence of any genuine results, we content ourselves with advancing a number of conjectures suggested by computer experiments. Finally, we connect the singular values of a trilinear form with the critical values of an associated family of a one parameter family of bilinear forms. Also here we have to offer mainly only experimental evidence.
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| 4. |
- Bondesson, Lennart, 1944-, et al.
(författare)
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The life and work of Olof Thorin (1912-2004)
- 2008
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Ingår i: Proceedings of the Estonian Academy of Sciences. - : Estonian Academy Publishers. - 1736-6046 .- 1736-7530. ; 57:1, s. 18-25
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Tidskriftsartikel (refereegranskat)abstract
- This paper reviews Olof Thorin's contributions to mathematical analysis, actuarial mathematics, and probability theory, though in reversed order. In probability theory he is known for his path-breaking work on infinite divisibility. In actuarial mathematics he contributed significantly to the ruin problem. However, his international fame very much relies on his work in mathematical analysis and his share in the Riesz-Thorin theorem. Data about his life and some personal recollections are also given.
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| 5. |
- Carro, Maria J., et al.
(författare)
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Some real interpolation methods for families of Banach spaces : a comparison
- 1997
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Ingår i: Journal of Approximation Theory. - : Elsevier BV. - 0021-9045 .- 1096-0430. ; 89:1, s. 26-57
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Tidskriftsartikel (refereegranskat)abstract
- We consider certain real interpolation methods for families of Banach spaces. We also define some new such methods obtained by passing to the limit in the constructions of Sparr and Cobos-Peetre. The relations between all these methods are studied. Characterizations of minimal and maximal spaces are obtained. Some concrete examples as well as sharp estimates of the corresponding operator norms are also exhibited.
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| 6. |
- Cobos, Fernando, et al.
(författare)
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Multilinear forms of Hilbert type and some other distinguished forms
- 2006
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Ingår i: Integral Equations and Operator Theory. - : Springer Science and Business Media LLC. - 1420-8989 .- 0378-620X. ; 56:1, s. 57-70
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Tidskriftsartikel (refereegranskat)abstract
- We give some new examples of bounded multilinear forms on the Hilbert spaces l(2) and L-2(0, infinity). We characterize those which are compact or Hilbert-Schmidt. In particular, we study m-linear forms (m >= 3) on l(2) which can be regarded as the multilinear analogue of the famous Hilbert matrix. We also determine the norm of the permanent on K-n, where K = R or C.
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| 7. |
- Cobos, Fernando, et al.
(författare)
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On the connection between real and complex interpolation of quasi-banach spaces
- 1998
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Ingår i: Bulletin des Sciences Mathématiques. - 0007-4497 .- 1952-4773. ; 122:1, s. 17-37
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Tidskriftsartikel (refereegranskat)abstract
- We describe a new approach to interpolate by the complex method quasi-Banach couples formed by real-intermediate spaces. End-point cases are also considered, and applications are given to function spaces and to operator spaces.
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| 8. |
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| 9. |
- Englis, Miroslav, et al.
(författare)
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On the formula of Jacques-Louis Lions for reproducing kernels of harmonic and other functions
- 2004
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Ingår i: Journal für die Reine und Angewandte Mathematik. - : Walter de Gruyter GmbH. - 0075-4102 .- 1435-5345. ; 570, s. 89-129
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Tidskriftsartikel (refereegranskat)abstract
- In an earlier work, J.-L. Lions produced a means for creating reproducing formulas for the space of harmonic functions with Sobolev boundary values on a domain in real Euclidean space. The present authors give a new proof of this result and also generalize the Lions formula to handle spaces of functions that are annihilated by an elliptic operator. The method of constructing the reproducing kernels seems to be based on the old paradigm of Aronszajn and Bergman. It is interesting to note that this model---that the kernel should take the form $$ K(x,y)=\sum_j e_j(x)·e_j(y) $$ for a suitable orthonormal basis $\{e_j\}$---goes back to the thesis of Bochner. That thesis well predates the early work of Bergman and Szegö.
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| 10. |
- Gustavsson, Jan, et al.
(författare)
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A submultiplicative function
- 1989
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Ingår i: Indagationes mathematicae (Proceedings). - : Elsevier BV. - 1385-7258. ; 92:4, s. 435-442
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Tidskriftsartikel (refereegranskat)
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