Summary
This paper contains proofs of the closure of certain sets of rational functions in various spaces. Thus, for example, conditions are derived for the closure of the sequence (x2 + z 2v )−1 in the space L2(0, ∞), and for the set\(\frac{{ct - z_v }}{{1 - \bar ctz_v }}\) in C(−1, +1). Analogous results are proved for other related sets of rational functions. Some of these results are new; others are new proofs of known theorems. The main point is that a uniform method is used throughout this paper. For a description of the method see article 1.
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Questo lavoro pervenne in redazione il primo giugno 1952 e l'A. rivide le prime 17 pagine delle bozze. A causa della Sua morte, improvvisamente avvenuta il 19 settembre 1952 a Montreux (Svizzera) l'ulteriore lavoro di revisione fu assunto dal Prof.H. David Lipsich.
Gli Annali di Matematica rivolgono un commosso pensiero alla memoria del loro collaboratoreOtto Szász ben noto nel mondo matematico internazionale.
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Szász, O. On closed sets of rational functions. Annali di Matematica 34, 195–218 (1953). https://doi.org/10.1007/BF02415331
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DOI: https://doi.org/10.1007/BF02415331