Complex analysis and convolution operators

Abstract

CONTENTS Chapter I. Analytic functionals § 1. Defining sets of analytic functionals § 2. Subharmonic functions § 3. Laplace transform of analytic functionals § 4. Convolution operators Chapter II. Surjectivity of convolution operators in the one-dimensional case § 5. A review of studies on the problem of the surjectivity of convolution operators § 6. Solvability of non-homogeneous convolution equations in convex domains in the complex plane Chapter III. Surjectivity of convolution operators in the multidimensional case § 7. Geometry of a convex domain § 8. Construction of a special entire function which is not of completely regular growth § 9. Estimates of indicators of subharmonic functions §10. A solvability criterion for non-homogeneous convolution equations in convex domains in Chapter IV. Homogeneous convolution equations §11. Approximation of subharmonic and plurisubharmonic functions §12. Polynomial approximation of entire functions §13. Approximation of solutions of a homogeneous convolution equation §14. Extension of solutions of a homogeneous convolution equation References