# Good-irreducible inner functions on a polydisc

Annales de l'institut Fourier (1979)

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

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topSawyer, 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

top- [1]P. R. AHERN, Singular sets of inner functions, Indiana Univ. Math. J., 21 (1971), 147-155. Zbl0235.32007MR46 #9390
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- [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]O. FROSTMAN, Potentiel d'équilibre et capacité des ensembles..., Lunds Univ. Mat. Sem. d., (1935), 1-118. Zbl0013.06302JFM61.1262.02
- [5]L. L. HELMS, Introduction to Potential Theory, Wiley-Interscience, 1969. Zbl0188.17203MR41 #5638
- [6]E. A. NORDGREN, Composition operators, Can. J. Math., 20 (1968), 442-449. Zbl0161.34703MR36 #6961
- [7] W. RUDIN, Function Theory in Polydiscs, Benjamin, 1969. Zbl0177.34101MR41 #501
- [8] W. RUDIN and P. R. AHERN, Factorizations of bounded holomorphic functions, Duke Math. J., 39 (1972), 767-777. Zbl0265.32004MR46 #9377
- [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]J. V. RYFF, Subordinate Hp functions, Duke Math. J., 33 (1966), 347-354. Zbl0148.30205MR33 #289
- [11]E. SAWYER, Inner functions on polydiscs, Ph. D. thesis, McGill University (1977).
- [12]M. TSUJI, Potential Theory in Modern Function Theory, Chelsea Publ. Co. Zbl0322.30001
- [13]A. ZYGMUND, Trigonometric Series, 2nd ed., Cambridge Univ. Press, 1959. Zbl0085.05601

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