Area Nevanlinna type classes of analytic functions in the unit disk and related spaces
Romi Shamoyan; Seraphim Maksakov
Communications in Mathematics (2018)
- Volume: 26, Issue: 1, page 47-76
- ISSN: 1804-1388
Access Full Article
topAbstract
topHow to cite
topReferences
top- Avetisyan, K., On representation of some classes of subharmonic functions in the unit disk and in the half plane, Izv. Nats. Acad. Armenii, Matematika., 29, 1, 1994, 1-13, (In Russian). (1994) MR1438866
- Bednazh, V.A., Karbanovich, O.V., Shamoyan, F.A., On some weighted spaces of meromorphic functions with restrictions of the Nevanlinna characteristic, Modern problems of complex and harmonic analysis: Abstracts of conference, Bryansk St. Univ., 2014, p. 56, (In Russian). (2014)
- Beller, E., 10.1007/BF02757275, Israel Jour. Math., 22, 1975, 68-80, 1. (1975) MR0385103DOI10.1007/BF02757275
- Beller, E., Factorization for non-Nevanlinna classes of analytic functions, Israel Jour. Math., 27, 3--4, 1977, 320-330, (1977) MR0442234
- Chyzhykov, I.E., Growth of analytic functions in the unit disc and complete measure in the sense of Grishin, Mat. Stud., 29, 1, 2008, 35-44, (2008) MR2424597
- Chyzhykov, I.E., 10.1090/S0002-9939-2012-11463-7, Proc. Amer. Math. Soc., 141, 2013, 1297-1311, (2013) MR3008877DOI10.1090/S0002-9939-2012-11463-7
- Chyzhykov, I.E., Growth of -th means of analytic and subharmonic function in the unit disk and angular distribution of zeros, arXiv:1509.02141, 2015, 1-19, (2015) MR2385361
- Chyzhykov, I.E., Skaski, S., Growth, zero distribution and factorization of analytic functions of moderate growth in the unit disc, Blashke products and their applications, Fields Inst. Comm., 65, 2013, 159-173, (2013) MR3052292
- Djrbashian, M.M., On a problem of representation of analytic functions, Soobsch. Inst. Mat. i Meh. AN Arm. SSR, 2, 1948, 3-40, (In Russian). (1948)
- Djrbashian, M.M., On parametric representation of some classes of meromorphic functions in the unit disk, Dokl. AN SSSR., 157, 1964, 1024-1027, (in Russian). (1964)
- Djrbashian, M.M., Integral transforms and representation in complex plane, 1966, p. 671, Nauka, GITTL. Moscow, (In Russian). (1966)
- Djrbashian, M.M., The factorization theory of functions, meromorphic in the unit disk, Mat. Sb., 79, 121, 1969, 517-615, (In Russian). (1969)
- Djrbashian, A.M., Mikaelyan, G.V., On boundary properties of Blaschke type products, Izv. Nats. AN Armenii, Matematika, 26, 1991, 435-442, (In Russian). (1991) MR1328283
- Goldberg, A.A., Ostrovskii, I.V., On distribution of values of meromorphic functions, 1970, p. 457, Nauka. Moscow, (In Russian). (1970) MR0280720
- Hardy, G., Littlwood, J., Polia, G., Inequalities, 1948, p. 456, GITTL, Moscow, (In Russian). (1948) MR0083530
- Hayman, W., Meromorphic functions, 1966, p. 447, Mir, Moscow, (In Russian). (1966) MR0214768
- Heipler, A., 10.1007/BF02761820, Israel Jour. Math., 34, 1--2, 1979, 1-11, (1979) MR0571391DOI10.1007/BF02761820
- Kasyaniuk, S.Ya., On functions from and class in case of circular rings, Mat. Sb., 42, 84, 1957, 301-326, (In Russian). (1957)
- Krylov, V.I., On functions regular in half plane, Mat. Sb., 6, 48, 1939, 95-138, (In Russian). (1939)
- Kursina, I.S., Factorization and parametric representation of weighted classes of analytic functions: the thesis abstract, Voronezh State Univ., Voronezh, 4, 2000, 43-54, (In Russian). (2000)
- Matevosyan, G.U., On an factorization of functions meromorphic in multiconnected domains and applications, Izv. AN Armenii, Matematika, 9, 1974, 387-408, (In Russian). (1974)
- Matevosyan, G.U., An analogue of class in case of circular rings, Izv. AN Armenii, Matematika., 21, 2, 1977, 173-182, (In Russian). (1977)
- Nevanlinna, R., Single-Valued Analytic Functions, 1941, p. 388, Gostehizdat, Moscow, (In Russian). (1941)
- Ohlupina, O.V., Description of a class of subharmonic functions in the unit disk, whose Nevanlinna’s characteristic is in wheigted -spaces, Vestnik Samarskogo Univ., 9/1, 59, 2008, 108-120, (In Russian). (2008) MR2436023
- Ohlupina, O.V., Parametric representation of some classes of subharmonic functions in a half plane with characteristic from weighted -spaces, Vestnik Bryanskogo Univ., Bryansk State Univ., 4, 2010, 24-36, (In Russian). (2010)
- Ohlupina, O.V., Green type potentials and integral representation of wheigted classes of subharmonic functions: the PhD thesis abstract, 38, 2012, 56-77, Saratov St. Univ., Saratov, (In Russian). (2012)
- Ortega-Cerda, J., Bruna, J., On -solutions of the Laplace equation and zeros of holomorphic functions, Annali della Scuola Normale de Pisa, 24, 1997, 571-591, (1997) MR1612330
- Prihodko, O.V., On root sets of some area Nevanlinna type spaces in angular domains on a complex plane, Vestnik Bryanskogo Univ. Bryansk State Univ., Bryansk, 4, 2010, 36-40, (In Russian). (2010)
- Privalov, I.I., Boundary properties of single-valued analytic functions, 1941, 206 p., Moscow St. Univ., Moscow, (In Russian). (1941) MR0047765
- Privalov, I.I., Boundary properties of analytic functions, 1950, 337 p., Gostekhizdat, Moscow and Leningrad, (In Russian). (1950) MR0047765
- Privalov, I.I., Kuznetsov, P.I., Boundary properties and various classes of harmonic and subharmonic functions, defined in arbitrary domains, Mat. Sbornik, 6, 48, 1939, 345-376, (In Russian). (1939)
- Rodikova, E.G., Factorization and description of zero sets of a class of functions, analytic in the unit disk, Sib. Elektron. Mat. Izv., 11, 2014, 52-63, (In Russian). (2014) MR3488405
- Rodikova, E.G., Factorization, root sets and interpolation in weighted classes of analytic functions, 2014, 121 p., Bryansk, Dissertation, Bryansk, (2014) ,121 p. (In Russian). (2014)
- Rodikova, E.G., On zeros of analytic classes of Privalov, Abstracts of Saratov winter school, Saratov, 1, 39, 2012, 141-142, (In Russian). (2012)
- Seneta, E., Regularly varying functions, 1985, 141 p., Nauka, Moscow, (In Russian). (1985) MR0815924
- Shamoyan, F.A., Description of closed ideals and some issues of factorization in algebras of growing functions, analytic in the disk, Izv. Acad. nauk ArmSSR, Matematika, 5, 1970, 450-472, (In Russian). (1970) MR0291815
- Shamoyan, F.A., Djrbashian's factorization theorem and characterization of zeros of analytic functions in a disk with bounded growth rate, Izv. Acad. nauk ArmSSR, Matematika, 13, 1978, 405-422, (In Russian). (1978)
- Shamoyan, F.A., Some remarks to parametric representation of Nevanlinna-Djrbashian, Mat. zametki., 52, 1992, 128-140, (In Russian). (1992)
- Shamoyan, F.A., 10.1007/BF02677545, Sib. Math. Journ., 40, 1999, 1422-1440, (In Russian). (1999) MR1741095DOI10.1007/BF02677545
- Shamoyan, F.A., Weighted spaces of analytic functions with mixed norm, 2014, 250 p., Bryansk St. Univ., Bryansk, Bryansk State University Publishing House, (In Russian). (2014)
- Shamoyan, F.A., Bednazh, V.A., Karbanovich, O.V., On classes of analytic functions in a disk with a characteristic R. Nevanlinny and -characteristic of weighted spaces, Sib. Elektron. Mat. Izv., 12, 2015, 150-167, (In Russian). (2015) MR3493791
- Shamoyan, F.A., Bednazh, V.A., Prihodko, O.V., On zero sets of some weighted classes of analytc functions in the disk, Vesthik Bryanskogo Universiteta, Bryansk, 4, 2008, 85-92, (In Russian). (2008)
- Shamoyan, F.A., Rodikova, E.G., On characterization of root sets of a weighted class of analytic functions in a disk, Vladikavkaz Mat. Jour., 16, 3, 2014, 64-75, (In Russian). (2014) MR3540665
- Shamoyan, F.A., Shubabko, E.N., 10.1007/978-3-0348-8378-8_26, Complex Analysis, Operators, and Related Topics, Oper. Theory Adv. Appl, 113, 2000, 331-338, (In Russian). (2000) MR1771772DOI10.1007/978-3-0348-8378-8_26
- Shamoyan, F.A., Shubabko, E.N., On a class of holomorphic functions in a disk, Zapiski Nauchnykh Seminarov POMI., 282, 2001, 244-255, (In Russian). (2001) MR1874891
- Shamoyan, F.A., Shubabko, E.N., Introduction in the theory of -classes of meromorphic functions, 2009, 152 p, Bryansk State University Publishing House, (In Russian). (2009)
- Shamoyan, R.F., On new parametric representations of analytic area Nevanlinna type classes in a circular ring on a complex plane , Jour. Sib. Fed. Univ. Math. Phys., 6, 1, 2013, 114-119, (2013) MR3168451
- Shamoyan, R.F., Li, H., Descriptions of zero sets and parametric representations of certain new analytic area Nevanlinna type spaces in the unit disk, Kragujevac Journal of Mathematics, 34, 2010, 73-89, (2010) MR2897897
- Shamoyan, R.F., Mihic, O.R., On zeros of some analytic spaces of area Nevanlinna type in halfplane, Trudy Petrozavodsk St. Univ., Matematika., 17, 2010, 67-72, (2010) MR3260491
- Shamoyan, R.F., Mihic, O.R., On some new theorems on certain analytic and meromorphic classes of Nevanlinna type on the complex plane, Kragujevac Math. Journal, 37, 1, 2013, 65-85, (2013) MR3073698
- Shamoyan, R.F., Mihic, O.R., 10.5937/KgJMath1402229S, Kragujevac Math. Journal, 38, 2, 2014, 229-244, (2014) MR3301453DOI10.5937/KgJMath1402229S
- Shamoyan, R., Shipka, A., Integral operators, embedding theorems and Taylor coefficients of area Nevanlinna type spaces of several variables and related problems, 2018, Preprint.. (2018)
- Shvedenko, S.V., Canonical products of Blashke type for spaces of area Nevanlinna type, Mat. Zametki., 37, 2, 1985, 212-219, (In Russian). (1985) MR0784366
- Shvedenko, S.V., The Hardy classes and related spaces of analytic functions in the unit circle, in the ball and in the polydisk, Itogi nauki i tehniki, Mat. analiz., 23, 1985, 3-124, (1985) MR0824267
- Stein, E., Singular integrals and differentiability properties of functions, 1970, 290 p., Princeton Univ. Press, New Jersey, (1970) Zbl0207.13501MR0290095
- Tsuji, M., Canonical product for a meromorphic functions in a unit circle, Journ. Math. Jap., 8, 1, 1956, 7-19, (1956) MR0103273
- Tsuji, M., Potential Theory in modern function theory, 1959, p. 345, Maruzen, Tokyo, (1959) MR0114894
- Zmorovich, V., On certain spaces of analytic functions in circular rings, Mat. Sbornik, 32, 1953, 643-652, (In Russian). (1953) MR0055448