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About the Blaschke products in polydiscs

M. E. Durakov

Institute of Mathematics and Computer Science, Siberian Federal University, Krasnoyarsk



Аннотация: We consider multidimensional analogs of Blaschke’s products. The motivation for this consideration was the articles by D. Alpay and A. Iger in connection with the interpolation theory in some functional spaces (Hilbert, Hardy, etc.). We construct the Blaschke multipliers using the Rudin characterization [5] of interior functions in polydics and the Lee-Yang polynomials from the theory of phase transitions in statistical mechanics [1][2]. As shown by M. Passare and A. Tsikh in [3], the amoeba of the Lee-Yang polynomial adjoins the log-image of a unit polydisc only on the skeleton of the polydisc. The main result of my talk is a theorem about the construction of a multidimensional Blaschke multiplier in odd-dimensional spaces. In such spaces, the Lee-Yang polynomial naturally decomposes into the sum of two polynomials that make up the inner rational function in the polydisc. The description of the permissible denominators of inner rational functions is made by the language of the polar [4] of the real cube $[-1,1]^n$.

Язык доклада: английский

Website: https://us02web.zoom.us/j/2162766238?pwd=TTBraGwvQ3Z3dWVpK3RCSFNMcWNNZz09

Список литературы
  1. C. N. Yang, T. D. Lee, “Statistical theory of equations of state and phase transitions. I. Theory of condensation”, Phys. Rev. (2), 87 (1952), 404–409  mathscinet
  2. T. D. Lee, C. N. Yang, “Statistical theory of equations of state and phase transitions. II. Lattice gas and Ising model”, Phys. Rev. (2), 87 (1952), 410–419  mathscinet
  3. M. Passare, A. Tskih, “Amoebas: their spines and their contours”, Idempotent mathematics and mathematical physics, Contemp. Math., 377, Amer. Math. Soc., Providence, RI, 2005, 275–288  mathscinet
  4. R. T. Rockafellar, Convex analysis, Princeton Mathematical Series, No. 28, Princeton University Press, Princeton, N.J., 1970  mathscinet
  5. W. Rudin, Function theory in polydiscs, W. A. Benjamin, Inc., New York-Amsterdam, 1969  mathscinet


* ID: 216 276 6238, password: residue


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