Geodesic
A question by Alexei Aleksandrov and logarithmic determinants
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 8 (2001) no. 3, pp. 308-317 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We construct an analytic function $f$ of Smirnov's class in the unit disk such that $\mathrm{Re}\,f$ vanishes almost everywhere on the unit circle and $$ \liminf_{t\to\infty} t\operatorname{meas}\{\zeta:\,|\zeta|=1,\ |f(\zeta)|\ge t\}=0. $$ This answers negatively to the question posed by A. Aleksandrov. We also find new sufficient conditions for representations of functions of Smirnov's class by the Schwarz and Cauchy integrals. These conditions extend previous results by Aleksandrov. 
@article{JMAG_2001_8_3_a5,
     author = {Mikhail Sodin},
     title = {A question by {Alexei} {Aleksandrov} and logarithmic determinants},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {308--317},
     year = {2001},
     volume = {8},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2001_8_3_a5/}
}
TY  - JOUR
AU  - Mikhail Sodin
TI  - A question by Alexei Aleksandrov and logarithmic determinants
JO  - Žurnal matematičeskoj fiziki, analiza, geometrii
PY  - 2001
SP  - 308
EP  - 317
VL  - 8
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/JMAG_2001_8_3_a5/
LA  - en
ID  - JMAG_2001_8_3_a5
ER  - 
%0 Journal Article
%A Mikhail Sodin
%T A question by Alexei Aleksandrov and logarithmic determinants
%J Žurnal matematičeskoj fiziki, analiza, geometrii
%D 2001
%P 308-317
%V 8
%N 3
%U http://geodesic.mathdoc.fr/item/JMAG_2001_8_3_a5/
%G en
%F JMAG_2001_8_3_a5
Mikhail Sodin. A question by Alexei Aleksandrov and logarithmic determinants. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 8 (2001) no. 3, pp. 308-317. http://geodesic.mathdoc.fr/item/JMAG_2001_8_3_a5/