124
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Linear differential equations with solutions lying in weighted Fock spaces

, , &
Pages 194-208 | Received 27 Sep 2018, Accepted 28 Dec 2019, Published online: 10 Jan 2020

References

  • Carlson R. Eigenfunctions of periodic differential operators analytic in a strip. Complex Anal Oper Theory. 2019;13(3):1111–1131. doi: 10.1007/s11785-018-0842-1
  • Carlson R. Analytic differential operators on the unit disk. Complex Anal Oper Theory. 2019;13(4):2017–2047. doi: 10.1007/s11785-019-00907-0
  • Choe H, Zhu K. Fock-Sobolev spaces and their Carleson measures. J Funct Anal. 2012;263(8):2483–2506. doi: 10.1016/j.jfa.2012.08.003
  • Chyzhykov I, Gundersen G, Heittokangas J. Linear differential equations and logarithmic derivative estimates. Proc Lond Math Soc. 2003;86(3):735–754. doi: 10.1112/S0024611502013965
  • Constantin O, Peláez J. Integral operators, embedding theorems and a Littlewood-Paley formula on weighted Fock spaces. J Geom Anal. 2016;26:1109–1154. doi: 10.1007/s12220-015-9585-7
  • Gröhn J. New applications of Picard's successive approximations. Bull Sci Math. 2011;135(5):475–487. doi: 10.1016/j.bulsci.2011.03.006
  • Gröhn J, Huusko J-M, Rättyä J. Linear differential equations with slowly growing solutions. Trans Amer Math Soc. 2018;370(10):7201–7227. doi: 10.1090/tran/7265
  • Guo K, Izuchi K. Composition operators on Fock type spaces. Acta Sci Math (Szeged). 2008;74:805–826.
  • Hai PV, Putinar M. Complex symmetric differential operators on Fock space. J Differential Equations. 2018;265(9):4213–4250. doi: 10.1016/j.jde.2018.06.003
  • Heittokangas J, Korhonen R, Rättyä J. Growth estimates for solutions of linear complex differential equations. Ann Acad Sci Fenn Math. 2004;29:233–246.
  • Heittokangas J, Korhonen R, Rättyä J. Growth estimates for solutions of non-homogeneous linear complex differential equations. Ann Acad Sci Fenn Math. 2009;34(1):145–156.
  • Heittokangas J, Korhonen R, Rättyä J. Linear differential equations with coefficients in weighted Bergman and Hardy spaces. Trans Amer Math Soc. 2008;360(2):1035–1056. doi: 10.1090/S0002-9947-07-04335-8
  • Heittokangas J, Korhonen R, Rättyä J. Linear differential equations with solutions in the Dirichlet type subspace of the Hardy space. Nagoya Math J. 2007;187(887):91–113. doi: 10.1017/S0027763000025861
  • Heittokangas J. On complex differential equations in the unit disc. Ann Acad Sci Fenn Math Diss. 2000;122:1–54.
  • Hu ZJ. Equivalent norms on Fock spaces with some application to extended Cesaro operators. Proc Amer Math Soc. 2013;141:2829–2840. doi: 10.1090/S0002-9939-2013-11550-9
  • Huusko J-M, Korhonen T, Reijonen A. Linear differential equations with solutions in the growth space Hω∞. Ann Acad Sci Fenn Math. 2016;41(1):399–416. doi: 10.5186/aasfm.2016.4128
  • Laine I. Nevanlinna theory and complex differential equations. Berlin: Walter de Gruyter; 1993.
  • Li H, Wulan H. Linear differential equations with solutions in the QK spaces. J Math Anal Appl. 2011;375(2):478–489. doi: 10.1016/j.jmaa.2010.09.028
  • Mengestie T. A note on the differential operator on generalized Fock spaces. J Math Anal Appl. 2018;458(2):937–948. doi: 10.1016/j.jmaa.2017.10.008
  • Mengestie T, Ueki S. Integral, differential and multiplication operators on weighted Fock spaces. Complex Anal Oper Theory. doi:10.1007/s11785-018-0820-7
  • Peláez J, Rättyä J. Weighted Bergman spaces induced by rapidly increasing weights. Mem Amer Math Soc. 2014;227:1066.
  • Pommerenke Ch. On the mean growth of the solutions of complex linear differential equations in the disk. Complex Var Theory Appl. 1982;1(1):23–38.
  • Xiao L. Differential equations with solutions lying in the F(p,q,s) space. Complex Var Elli Equ. 2018;63(1):116–135. doi: 10.1080/17476933.2017.1288724
  • Yang D, Tu J. Linear differential equations with coefficients in Fock type space. Electron J Qual Theory Differ Equ. 2011;22(48):1–10. doi: 10.14232/ejqtde.2011.1.48
  • Zhu K. Analysis on Fock spaces. New York: Springer; 2012.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.