Restrictions of continuous functions |
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Authors: | Jean-Pierre Kahane Yitzhak Katznelson |
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Institution: | (1) Departamento de Matematica, Universidade Estadual de Santa Cruz, Ilheus-Ba, Brazil;(2) Departments of Mathematics and of Computer Science, Ben-Gurion University, Beer Sheva, 84105, Israel;(3) Departamento de Matematica, Universidade Federal do Ceara, Fortaleza-Ce, Brazil;(4) Department of Mathematics, University of Texas at Austin, 1 University Station C1200, Austin, TX 78712-0257, USA |
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Abstract: | Let α = {α1, ...,αk} be a finite multiset of non-negative real numbers. Consider the sequence of all positive integer multiples of all α i ’s, and note the multiplicity of each term in this sequence. This sequence of multiplicities is the resonance sequence generated by {α 1, ...,αk}. Two multisets are combinatiorially equivalent if they generate the same resonance sequence. The paper is devoted to the classification of multisets up to combinatorial equivalence. We show that the problem of combinatorial equivalence of multisets is closely related to the problem of classification of systems of second order ordinary differential equations up to focal equivalence. |
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