Mathematics Subject Classification 1991

30-XX Functions of a complex variable, {For analysis on manifolds, See 58-XX} ( 0 Dok.)

• 30-00 General reference works (handbooks, dictionaries, bibliographies, etc.) ( 0 Dok.)
• 30-01 Instructional exposition (textbooks, tutorial papers, etc.) ( 0 Dok.)
• 30-02 Research exposition (monographs, survey articles) ( 0 Dok.)
• 30-03 Historical (must be assigned at least one classification number from Section 01) ( 0 Dok.)
• 30-04 Explicit machine computation and programs (not the theory of computation or programming) ( 0 Dok.)
• 30-06 Proceedings, conferences, collections, etc. ( 0 Dok.)
• 30Axx General properties ( 0 Dok. )
• 30A05 Monogenic properties of complex functions (including polygenic and areolar monogenic functions) ( 0 Dok.)
• 30A10 Inequalities in the complex domain ( 0 Dok.)
• 30A99 None of the above but in this section ( 0 Dok.)
• 30Bxx Series expansions ( 0 Dok. )
• 30B10 Power series (including lacunary series) ( 0 Dok.)
• 30B20 Random power series ( 0 Dok.)
• 30B30 Boundary behavior of power series, over-convergence ( 0 Dok.)
• 30B40 Analytic continuation ( 0 Dok.)
• 30B50 Dirichlet series and other series expansions, exponential series, See also {11M41, 42-XX} ( 0 Dok.)
• 30B60 Completeness problems, closure of a system of functions ( 0 Dok.)
• 30B70 Continued fractions, See also {11A55, 40A15} ( 0 Dok.)
• 30B99 None of the above but in this section ( 0 Dok.)
• 30Cxx Geometric function theory ( 0 Dok. )
• 30C10 Polynomials ( 0 Dok.)
• 30C15 Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of functions with bounded Dirichlet integral), {For algebraic theory, See 12D10; for real methods, See 26C10} ( 0 Dok.)
• 30C20 Conformal mappings of special domains ( 0 Dok.)
• 30C25 Covering theorems in conformal mapping theory ( 0 Dok.)
• 30C30 Numerical methods in conformal mapping theory, See Also { 65E05} ( 0 Dok.)
• 30C35 General theory of conformal mappings ( 0 Dok.)
• 30C40 Kernel functions and applications ( 0 Dok.)
• 30C45 Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.) ( 0 Dok.)
• 30C50 Coefficient problems for univalent and multivalent functions ( 0 Dok.)
• 30C55 General theory of univalent and multivalent functions ( 0 Dok.)
• 30C62 Quasiconformal mappings in the plane ( 0 Dok.)
• 30C65 Quasiconformal mappings in $R^n$, other generalizations ( 0 Dok.)
• 30C70 Extremal problems for conformal and quasiconformal mappings, variational methods ( 0 Dok.)
• 30C75 Extremal problems for conformal and quasiconformal mappings, other methods ( 0 Dok.)
• 30C80 Maximum principle; Schwarz's lemma, Lindelof principle, analogues and generalizations; subordination ( 0 Dok.)
• 30C85 Capacity and harmonic measure in the complex plane, See also {31A15} ( 0 Dok.)
• 30C99 None of the above but in this section ( 0 Dok.)
• 30Dxx Entire and meromorphic functions, and related topics ( 0 Dok. )
• 30D05 Functional equations in the complex domain, iteration and composition of analytic functions, See also {34A20, 39-XX, 58F08, 58F23} ( 0 Dok.)
• 30D10 Representations of entire functions by series and integrals ( 0 Dok.)
• 30D15 Special classes of entire functions and growth estimates ( 0 Dok.)
• 30D20 Entire functions, general theory ( 0 Dok.)
• 30D30 Meromorphic functions, general theory ( 0 Dok.)
• 30D35 Distribution of values, Nevanlinna theory ( 0 Dok.)
• 30D40 Cluster sets, prime ends, boundary behavior ( 0 Dok.)
• 30D45 Bloch functions, normal functions, normal families ( 0 Dok.)
• 30D50 Blashke products, bounded mean oscillation, bounded characteristic, bounded functions, functions with positive real part ( 0 Dok.)
• 30D55 ${H}^p$-classes ( 0 Dok.)
• 30D60 Quasi-analytic and other classes of functions ( 0 Dok.)
• 30D99 None of the above but in this section ( 0 Dok.)
• 30Exx Miscellaneous topics of analysis in the complex domain ( 0 Dok. )
• 30E05 Moment problems, interpolation problems ( 0 Dok.)
• 30E10 Approximation in the complex domain ( 0 Dok.)
• 30E15 Asymptotic representations in the complex domain ( 0 Dok.)
• 30E20 Integration, integrals of Cauchy type, integral representations of analytic functions, See also {45Exx} ( 0 Dok.)
• 30E25 Boundary value problems, See also {45Exx} ( 0 Dok.)
• 30E99 None of the above but in this section ( 0 Dok.)
• 30Fxx Riemann surfaces ( 0 Dok. )
• 30F10 Compact Riemann surfaces and uniformization, See Also {14H15, 32G15} ( 0 Dok.)
• 30F15 Harmonic functions on Riemann surfaces ( 0 Dok.)
• 30F20 Classification theory of Riemann surfaces ( 0 Dok.)
• 30F25 Ideal boundary theory ( 0 Dok.)
• 30F30 Differentials on Riemann surfaces ( 0 Dok.)
• 30F35 Fuchsian groups and automorphic functions, See also {11Fxx, 20H10, 22E40, 32Gxx, 32Nxx} ( 0 Dok.)
• 30F40 Kleinian groups, See also {20H10} ( 0 Dok.)
• 30F45 Conformal metrics (hyperbolic, Poincare, distance functions) ( 0 Dok.)
• 30F50 Klein surfaces ( 0 Dok.)
• 30F60 Teichmuller theory, See also {32G15} ( 0 Dok.)
• 30F99 None of the above but in this section ( 0 Dok.)
• 30Gxx Generalized function theory ( 0 Dok. )
• 30G06 Non-Archimedean function theory, See also {12J25}; nonstandard function theory, See also {03H05} ( 0 Dok.)
• 30G12 Finely holomorphic functions and topological function theory ( 0 Dok.)
• 30G15 Topological function theory ( 0 Dok.)
• 30G20 Generalizations of Bers or Vekua type (pseudoanalytic, $p$-analytic, etc.) ( 0 Dok.)
• 30G25 Discrete analytic functions ( 0 Dok.)
• 30G30 Other generalizations of analytic functions (including abstract-valued functions) ( 0 Dok.)
• 30G35 Functions of hypercomplex variables and generalized variables ( 0 Dok.)
• 30G99 None of the above but in this section ( 0 Dok.)
• 30H05 Spaces and algebras of analytic functions, See also {32E25, 46Exx, 46J15} ( 0 Dok.)