Geodesic
On quadratic forms generated by the Neumann functions
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 29, Tome 429 (2014), pp. 157-177 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Quadratic forms depending on the values of Neumann functions are studied. Monotonic behavior under extension of domain and polarization was proved. Also the behavior of this quadratic form under conformal univalent mapping was researched. As an application, the distortion theorem generalizing the results of Dubinin, Kim in the case of finitely connected domain are derived. 
@article{ZNSL_2014_429_a11,
     author = {E. G. Prilepkina},
     title = {On quadratic forms generated by the {Neumann} functions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {157--177},
     year = {2014},
     volume = {429},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_429_a11/}
}
TY  - JOUR
AU  - E. G. Prilepkina
TI  - On quadratic forms generated by the Neumann functions
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2014
SP  - 157
EP  - 177
VL  - 429
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2014_429_a11/
LA  - ru
ID  - ZNSL_2014_429_a11
ER  - 
%0 Journal Article
%A E. G. Prilepkina
%T On quadratic forms generated by the Neumann functions
%J Zapiski Nauchnykh Seminarov POMI
%D 2014
%P 157-177
%V 429
%U http://geodesic.mathdoc.fr/item/ZNSL_2014_429_a11/
%G ru
%F ZNSL_2014_429_a11
E. G. Prilepkina. On quadratic forms generated by the Neumann functions. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 29, Tome 429 (2014), pp. 157-177. http://geodesic.mathdoc.fr/item/ZNSL_2014_429_a11/

[1] G. M. Goluzin, Geometricheskaya teoriya funktsii kompleksnogo peremennogo, Nauka, M., 1966 | MR | Zbl

[2] Z. Nehary, “Some inequalities in the theory of functions”, Trans. Amer. Math., 75:2 (1953), 256–286 | DOI | MR

[3] P. Duren, M. M. Schiffer, “Robin functions and energy functionals of multiply connected domains”, Pacific J. Math., 148:2 (1991), 251–273 | DOI | MR | Zbl

[4] P. Duren, M. M. Schiffer, “Robin functions and distortion of capacity under conformal mapping”, Complex Variables, 21 (1993), 189–196 | DOI | MR | Zbl

[5] V. N. Dubinin, “O kvadratichnykh formakh, porozhdennykh funktsiyami Grina i Robena”, Mat. sb., 200:10 (2009), 25–38 | DOI | MR | Zbl

[6] V. N. Dubinin, M. Vuorinen, “Robin functions and distortion theorems for regular mappings”, Math. Nachr., 283:11 (2010), 1589–1602 | DOI | MR | Zbl

[7] V. N. Dubinin, V. Yu. Kim, “Obobschennye kondensatory i teoremy o granichnom iskazhenii pri konformnom otobrazhenii”, Dalnevost. mat. zh., 13:2 (2013), 196–208 | Zbl

[8] V N. Dubinin, Emkosti kondensatorov i simmetrizatsiya v geometricheskoi teorii funktsii kompleksnogo peremennogo, Dalnauka, Vladivostok, 2009

[9] D. Karp, E. Prilepkina, “Reduced modules with free boundary and its applications”, Ann. Acad. Scient. Fenn., 34 (2009), 353–378 | MR | Zbl

[10] E. G. Emelyanov, “O kvadratichnykh differentsialakh v mnogosvyaznykh oblastyakh, yavlyayuschikhsya polnymi kvadratami. II”, Zap. nauchn. semin. POMI, 350, 2007, 40–51 | MR

[11] P. Duren, J. Pfaltzgraff, E. Thurman, “Physical interpretation and further properties of Robin capacity”, Algebra i analiz, 9:3 (1997), 211–219 | MR | Zbl

[12] V. N. Dubinin, E. G. Prilepkina, “O sokhranenii obobschennogo privedennogo modulya pri geometricheskikh preobrazovaniyakh ploskikh oblastei”, Dalnevost. mat. zh., 6:1–2 (2005), 39–56

[13] E. G. Prilepkina, “O printsipakh kompozitsii dlya privedennykh modulei”, Sib. mat. zh., 52:6 (2011), 1357–1372 | MR | Zbl

[14] E. G. Prilepkina, “Teoremy iskazheniya dlya odnolistnykh funktsii v mnogosvyaznykh oblastyakh”, Dalnevost. mat. zh., 9:1–2 (2009), 140–149 | MR

[15] Ch. Pommerenke, Boundary behaviour of conformal maps, Springer-Verlag, 1992 | MR | Zbl