Leray-volevich conditions for systems of evolution equations basing on the generalized derivative in the sense of gelfond-leontjev

Abstract

Systems of evolution equations basing on the generalized derivative in the sense of Gelfond-Leontjev are considered. Using scale type estimates the sufficiency and necessity of Leray-Volevich conditions is discussed. The obtained estimates are weaker than in the special case basing on the classical complex derivative.

Keywords:

• entire functions of finite order
• growth estimates
• Leray-Volevich conditons
• derivative in the sense of Gelfond
• Leontjev
• scales of Banach spaces
• differential operators of infinite order

¹The second author was supported by INTAS.

¹The second author was supported by INTAS.

Notes

¹The second author was supported by INTAS.