Good-irreducible inner functions on a polydisc

Eric T. Sawyer

Annales de l'institut Fourier (1979)

  • Volume: 29, Issue: 2, page 185-210
  • ISSN: 0373-0956

Abstract

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An explicit formula is developed for Nevanlinna class functions whose behaviour at the boundary is “sufficiently rational” and is then used to deduce the uniqueness of the factorization of such inner functions. A generalization of a theorem of Frostman is given and the above results are then applied to the construction of good and/or irreducible inner functions on a polydisc.

How to cite

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Sawyer, Eric T.. "Good-irreducible inner functions on a polydisc." Annales de l'institut Fourier 29.2 (1979): 185-210. <http://eudml.org/doc/74407>.

@article{Sawyer1979,
abstract = {An explicit formula is developed for Nevanlinna class functions whose behaviour at the boundary is “sufficiently rational” and is then used to deduce the uniqueness of the factorization of such inner functions. A generalization of a theorem of Frostman is given and the above results are then applied to the construction of good and/or irreducible inner functions on a polydisc.},
author = {Sawyer, Eric T.},
journal = {Annales de l'institut Fourier},
keywords = {Blaschke product; factorization of inner functions; unit polydisc},
language = {eng},
number = {2},
pages = {185-210},
publisher = {Association des Annales de l'Institut Fourier},
title = {Good-irreducible inner functions on a polydisc},
url = {http://eudml.org/doc/74407},
volume = {29},
year = {1979},
}

TY - JOUR
AU - Sawyer, Eric T.
TI - Good-irreducible inner functions on a polydisc
JO - Annales de l'institut Fourier
PY - 1979
PB - Association des Annales de l'Institut Fourier
VL - 29
IS - 2
SP - 185
EP - 210
AB - An explicit formula is developed for Nevanlinna class functions whose behaviour at the boundary is “sufficiently rational” and is then used to deduce the uniqueness of the factorization of such inner functions. A generalization of a theorem of Frostman is given and the above results are then applied to the construction of good and/or irreducible inner functions on a polydisc.
LA - eng
KW - Blaschke product; factorization of inner functions; unit polydisc
UR - http://eudml.org/doc/74407
ER -

References

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  1. [1]P. R. AHERN, Singular sets of inner functions, Indiana Univ. Math. J., 21 (1971), 147-155. Zbl0235.32007MR46 #9390
  2. [2]A. BEURLING, On two problems concerning linear transformations in Hilbert space, Acta. Math., 81 (1949), 239-255. Zbl0033.37701MR10,381e
  3. [3]R. G. DOUGLAS, H. S. SHAPIRO, and A. L. SHIELDS, Cyclic vectors and invariant subspaces for the backward shift operator, Ann. Inst. Fourier, Grenoble, 20, 1 (1970), 37-76. Zbl0186.45302MR42 #5088
  4. [4]O. FROSTMAN, Potentiel d'équilibre et capacité des ensembles..., Lunds Univ. Mat. Sem. d., (1935), 1-118. Zbl0013.06302JFM61.1262.02
  5. [5]L. L. HELMS, Introduction to Potential Theory, Wiley-Interscience, 1969. Zbl0188.17203MR41 #5638
  6. [6]E. A. NORDGREN, Composition operators, Can. J. Math., 20 (1968), 442-449. Zbl0161.34703MR36 #6961
  7. [7] W. RUDIN, Function Theory in Polydiscs, Benjamin, 1969. Zbl0177.34101MR41 #501
  8. [8] W. RUDIN and P. R. AHERN, Factorizations of bounded holomorphic functions, Duke Math. J., 39 (1972), 767-777. Zbl0265.32004MR46 #9377
  9. [9]W. RUDIN and E. L. STOUT, Boundary properties of functions of several complex variables, J. Math. Mech., 14 (1965), 991-1006. Zbl0147.11601MR32 #230
  10. [10]J. V. RYFF, Subordinate Hp functions, Duke Math. J., 33 (1966), 347-354. Zbl0148.30205MR33 #289
  11. [11]E. SAWYER, Inner functions on polydiscs, Ph. D. thesis, McGill University (1977). 
  12. [12]M. TSUJI, Potential Theory in Modern Function Theory, Chelsea Publ. Co. Zbl0322.30001
  13. [13]A. ZYGMUND, Trigonometric Series, 2nd ed., Cambridge Univ. Press, 1959. Zbl0085.05601

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