| 1. |
- Aluffi, P., et al.
(författare)
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Plane curves with small linear orbits II
- 2000
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Ingår i: International Journal of Mathematics. - 0129-167X. ; 11:5, s. 591-608
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Tidskriftsartikel (refereegranskat)abstract
- The linear orbit of a plane curve of degree d is its orbit in p(d(d+3)/2) under the natural action of PGL(3). We classify curves with positive dimensional stabilizer, and we compute the degree of the closure of the linear orbits of curves supported on unions of lines. Together with the results of [3], this encompasses the enumerative geometry of all plane curves with small linear orbit. This information will serve elsewhere as an ingredient in the computation of the degree of the orbit closure of an arbitrary plane curve.
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| 2. |
- Josefson, Bengt
(författare)
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Approximations of holomorphic functions in certain banach spaces
- 2004
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Ingår i: International Journal of Mathematics. - 0129-167X. ; 15:5, s. 467-471
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Tidskriftsartikel (refereegranskat)abstract
- Let E be a Banach space and let B(R) ? E denote the open ball with centre at 0 and radius R. The following problem is studied: given 0 < r < R, ? > 0 and a function f holomorphic on B(R), does there always exist an entire function g on E such that abs(f - g) < ? on B (r)? L. Lempert has proved that the answer is positive for Banach spaces having an unconditional basis with unconditional constant 1. In this paper a somewhat shorter proof of Lemperts result is given. In general it is not possible to approximate f by polynomials since f does not need to be bounded on B(r).
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| 3. |
- Merker, Joël, et al.
(författare)
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Metrically Thin Singularities of Integrable CR Functions
- 2000
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Ingår i: International Journal of Mathematics. - 0129-167X. ; 11:7, s. 857-872
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Tidskriftsartikel (refereegranskat)abstract
- In this article, we consider metrically thin singularities E of the solutions of the tangential Cauchy-Riemann operators on a smoothly embedded Cauchy-Riemann manifold M (CR functions on M \ E). Our main result establishes the removability of E within the space of locally integrable functions on M, which are CR on M\E, under the hypothesis that the (dim M - 2)-dimensional Hausdorff volume of E is zero and that the CR-orbits of M and of M \ E are comparable. [ABSTRACT FROM AUTHOR
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