Abstract
Given two compact sets, E and F, on the unit circle, we study the class of subharmonic functions on the unit disk which can grow at the direction of E and F (sets of singularities) at different rate. The main result concerns the Blaschke-type condition for the Riesz measure of such functions. The optimal character of this condition is demonstrated.
To Victor Katsnelson on occasion of his 75th anniversary
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
P. Ahern, D. Clark, On inner functions with B p derivatives, Michigan Math. J. 23 (1976), 107–118.
W. Blaschke, Eine Erweiterung des Satzes von Vitali über Folgen analytischer Funktionen, S.-B. Säcks Akad. Wiss. Leipzig Math.-Natur. KI. 67 (1915), 194–200.
A. Borichev, L. Golinskii, S. Kupin, A Blaschke-type condition and its application to complex Jacobi matrices, Bull. Lond. Math. Soc. 41 (2009), 117–123.
A. Borichev, L. Golinskii, S. Kupin, On zeros of analytic functions satisfying non-radial growth conditions, Rev. Mat. Iberoam., 34, no. 3 (2018), 1153–1176.
L. Carleson, Sets of uniqueness for functions analytic in the unit disc, Acta Math., 87 (1952), 325–345.
S. Favorov, L. Golinskii, A Blaschke-Type condition for Analytic and Subharmonic Functions and Application to Contraction Operators, Amer. Math Soc. Transl. 226 (2009), 37–47.
S. Favorov, L. Golinskii, Blaschke-type conditions for analytic and subharmonic functions in the unit disk: local analogs and inverse problems, Comput. Methods Funct. Theory, 12 (2012) no. 1, 151–166.
J. Garnett, Bounded analytic functions, Graduate Texts in Mathematics, 236, Springer, New York, 2007.
J. Garnett, D. Marshall, Harmonic measure, Cambridge University Press, Cambridge, 2005.
B. Khabibullin, Z. Abdullina, A. Rozit, A uniqueness theorem and subharmonic test functions, Algebra I Analiz, 30 (2018) no. 2, 318–334.
B. Khabibullin, N. Tamindarova, Subharmonic test functions and the distribution of zero sets of holomorphic functions, Lobachevskii Journal of Math., 38 (2017) no. 1, 70–79.
R. Killip, B. Simon, Sum rules for Jacobi matrices and their applications to spectral theory, Ann. Math., 158 (2003), 253–321.
E. Lieb, M. Loss, Analysis, Graduate Studies in Mathematics, vol. 14, AMS, Providence, RI, 1997.
T. Ransford, Potential Theory in the Complex Plane, London Math. Soc. Student Texts, vol. 28, Cambridge University Press, 1995.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Favorov, S., Golinskii, L. (2020). On a Blaschke-Type Condition for Subharmonic Functions with Two Sets of Singularities on the Boundary. In: Alpay, D., Fritzsche, B., Kirstein, B. (eds) Complex Function Theory, Operator Theory, Schur Analysis and Systems Theory. Operator Theory: Advances and Applications(), vol 280. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-44819-6_12
Download citation
DOI: https://doi.org/10.1007/978-3-030-44819-6_12
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-44818-9
Online ISBN: 978-3-030-44819-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)