The Łojasiewicz Exponent at Infinity of Non-negative and Non-degenerate Polynomials
| dc.contributor.author | Oleksik, Grzegorz | |
| dc.contributor.author | Różycki, Adam | |
| dc.date.accessioned | 2021-10-22T06:02:55Z | |
| dc.date.available | 2021-10-22T06:02:55Z | |
| dc.date.issued | 2018 | |
| dc.identifier.citation | Oleksik, G., Różycki, A. The Łojasiewicz Exponent at Infinity of Non-negative and Non-degenerate Polynomials. Bull Braz Math Soc, New Series 49, 743–759 (2018). https://doi.org/10.1007/s00574-018-0078-8 | pl_PL |
| dc.identifier.issn | 1678-7544 | |
| dc.identifier.uri | http://hdl.handle.net/11089/39501 | |
| dc.description.abstract | Let f be a real polynomial, non-negative at infinity with non-compact zero-set. Suppose that f is non-degenerate in the Kushnirenko sense at infinity. In this paper we give a formula for the Łojasiewicz exponent at infinity of f and a formula for the exponent of growth of f in terms of its Newton polyhedron. | pl_PL |
| dc.language.iso | en | pl_PL |
| dc.publisher | Springer Nature | pl_PL |
| dc.relation.ispartofseries | Bulletin of the Brazilian Mathematical Society, New Series;49 | |
| dc.rights | Uznanie autorstwa 4.0 Międzynarodowe | * |
| dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | * |
| dc.subject | Kushnirenko nondegeneracy | pl_PL |
| dc.subject | Newton polyhedron | pl_PL |
| dc.subject | Łojasiewicz exponent | pl_PL |
| dc.title | The Łojasiewicz Exponent at Infinity of Non-negative and Non-degenerate Polynomials | pl_PL |
| dc.type | Article | pl_PL |
| dc.page.number | 743–759 | pl_PL |
| dc.contributor.authorAffiliation | Faculty of Mathematics and Computer Science, University of Lodz, S. Banacha 22, 90-238, Lodz, Poland | pl_PL |
| dc.contributor.authorAffiliation | Faculty of Mathematics and Computer Science, University of Lodz, S. Banacha 22, 90-238, Lodz, Poland | pl_PL |
| dc.identifier.eissn | 1678-7714 | |
| dc.references | Bùi, N.T.N., Pham, T.S.: Computation of the Łojasiewicz exponent of nonnegative and nondegenerate analytic functions. Int. J. Math. 25, 1450092 (2014) | pl_PL |
| dc.references | Đinh, S.T., Hà, H.V., Tháo, N.T.: Łojasiewicz inequality for polynomial functions on non-compact domains. Int. J. Math. 23, 1250033 (2012) | pl_PL |
| dc.references | Đinh, S.T., Kurdyka, K., Le Gal, O.: Łojasiewicz inequality on non-compact domains and singularities at infinity. Int. J. Math. 24, 1350079 (2013) | pl_PL |
| dc.references | Đinh, S.T., Hà, H.V., Pham, T.S., Tháo, N.T.: Global Łojasiewicz-type inequality for non-degenerate polynomial maps. J. Math. Anal. Appl. 410, 541–560 (2014) | pl_PL |
| dc.references | Gindikin, S.G.: Energy estimates connected with the Newton polyhedron. (Russian) Collection of articles dedicated to the memory of Ivan Georgievič Petrovskiĭ. Trudy Moskov. Mat. Obšč. 31, 189–236 (1974) | pl_PL |
| dc.references | Gwoździewicz, J.: Growth at infinity of a polynomial with a compact zero set. Banach Cent. Publ. 44, 123–128 (1998) | pl_PL |
| dc.references | Hà, H.V., Duc, N.H.: Łojasiewicz inequality at infinity for polynomials in two real variables. Math. Z. 266, 243–264 (2010) | pl_PL |
| dc.references | Hà, H.V., Ngai, H.V., Pham, T.S.: A global smooth version of the classical Łojasiewicz inequality. J. Math. Anal. Appl. 421, 1559–1572 (2015) | pl_PL |
| dc.references | Hörmander, L.: On the division of distributions by polynomials. Ark. Mat. 3, 555–568 (1958) | pl_PL |
| dc.references | Kollár, J.: Sharp effective Nullstellensatz. J. Am. Math. Soc. 1, 963–975 (1988) | pl_PL |
| dc.references | Łojasiewicz, S.: Sur le problème de la division. (French). Stud. Math. 18, 87–136 (1959) | pl_PL |
| dc.identifier.doi | 10.1007/s00574-018-0078-8 | |
| dc.subject.msc | 14P10 | |
| dc.discipline | matematyka | pl_PL |
Files in this item
This item appears in the following Collection(s)
Except where otherwise noted, this item's license is described as Uznanie autorstwa 4.0 Międzynarodowe