Open problems for entire functions of bounded index in direction 

Author 
andriykopanytsia@gmail.com, olskask@gmail.com
IvanoFrankivsk National Technical University of Oil and Gas, Ivan Franko National University of Lviv

Abstract 
This paper is devoted to some unsolved problems in the theory of entire functions of several
variables in connection with investigation of functions of bounded $L$index in direction.

Keywords 
entire function of several variables; bounded $L$index in direction; partial differential equation;
differential equation of infinite order

DOI 
doi:10.15330/ms.43.1.103109

Reference 
1. A.I. Bandura, O. B. Skaskiv, Entire functions of bounded $L$index in direction, Mat. Stud., 27 (2007),
¹1, 30–52. (in Ukrainian)
2. A.I. Bandura, O.B. Skaskiv, Sufficient sets for boundedness $L$index in direction for entire functions, Mat. Stud., 30 (2008), ¹2, 177–182. 3. A.I. Bandura, O.B. Skaskiv, Entire functions of bounded and unbounded index in direction, Mat. Stud., 27 (2007), ¹2, 211–215. (in Ukrainian) 4. G.H. Fricke, S.M. Shah, Entire functions satisfying a linear differential equation, Indag. Math., 37 (1975), 39–41. 5. A.D. Kuzyk, M.N. Sheremeta, On entire functions, satisfying linear differential equations, Diff. equations, 26 (1990), ¹10, 1716–1722. (in Russian) 6. S.M. Shah, Entire solutions of linear differential equations and bounds for growth and index numbers, Proc. Sect. A: Mathematics, Royal Soc. Edinburgh, 93A (1983), 49–60. 7. B. Lepson, Differential equations of infinite order, hyperdirichlet series and entire functions of bounded index, Proc. Sympos. Pure Math., V.2., Amer. Math. Soc.: Providence, Rhode Island, 1968, 298–307. 8. A.I. Bandura, A modified criterion of boundedness of Lindex in direction, Mat. Stud., 39 (2013), ¹1, 99–102. 9. A.I. Bandura, Sufficient conditions of boundedness Lindex in direction for entire functions with “planar” zeros of genus $p$, Mathem. bulletin SSS, 6 (2009), 44–49. (in Ukrainian) 10. A.I. Bandura, O.B. Skaskiv, Boundedness of $L$index in direction of functions of the form $f(\langle z, m\rangle)$ and existence theorems, Mat. Stud., 41 (2014), ¹1, 45–52. 
Pages 
103109

Volume 
43

Issue 
1

Year 
2015

Journal 
Matematychni Studii

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