Functions of Completely Regular Growth

Inhaltsverzeichnis

• 1. Entire functions of completely regular growth of one variable.
• §1. Preliminaries.
• §2. Regularity of growth, D’-convergence and right distribution of zeros.
• §3. Rays of completely regular growth. Addition of indicators.
• Notes.
• 2. Subharmonic functions of completely regular growth in Rn.
• §1. General information on subharmonic functions. D*-convergence ..
• §2. Criteria for regularity of growth in Rn.
• §3. Rays of completely regular growth and limit sets.
• §4. Addition of indicators.
• 3. Entire functions of completely regular growth in Cn.
• §1. Functions of c completely regular growth on complex rays.
• §2. Addition of indicators.
• §3. Entire functions with prescribed behaviour at infinity.
• 4. Functions of completely regular growth in the half-plane or a cone.
• §1. Preliminary information on functions holomorphic in a half-plane.
• §2. Functions of completely regular growth in C+.
• §3. Functions of completely regular growth in C+.
• §4. Functions of completely regular growth in a cone.
• 5. Functions of exponential type and bounded on the real space (Fourier transforms of distribution of compact support).
• §1. Regularity of growth of entire functions of exponential type and bounded on the real space.
• §2. Discrete uniqueness sets.
• §3. Norming sets.
• 6. Quasipolynomials.
• §1. M-quasipolynomials. Growth and zero distribution.
• §2. Entire functions that are quasipolynomials in every variable.
• §3. Factors of quasipolynomials.
• 7. Mappings.
• §1. Information on the general theory of holomorphic mappings.
• §2. Plurisubharmonic functions of ?-regular growth and asymptotic behaviour of order functions of holomorphic mappings.
• §3. Jessen’s theorem for almost periodic holomorphic mappings.