| 30-XX | | Prev: 28 | Up: Top | Next: 31 | |
| Functions of a complex variable | |
| {For analysis on manifolds, see 58-XX} |
30-00
| General reference works (handbooks, dictionaries, bibliographies, etc.)
| 30-01
| Instructional exposition (textbooks, tutorial papers, etc.)
| 30-02
| Research exposition (monographs, survey articles)
| 30-03
| Historical (must also be assigned at least one classification number from Section 01)
| 30-04
| Explicit machine computation and programs (not the theory of computation or programming)
| 30-06
| Proceedings, conferences, collections, etc.
| |
30Axx
| General properties
| 30A05 |
Monogenic properties of complex functions (including polygenic and areolar monogenic functions)
| 30A10 |
Inequalities in the complex domain
| 30A99 |
None of the above, but in this section
| |
30Bxx
| Series expansions
[xref: 11N30]
| 30B10 |
Power series (including lacunary series)
| 30B20 |
Random power series
| 30B30 |
Boundary behavior of power series, over-convergence
| 30B40 |
Analytic continuation
| 30B50 |
Dirichlet series and other series expansions, exponential series [See also 11M41, 42-XX]
| 30B60 |
Completeness problems, closure of a system of functions
| 30B70 |
Continued fractions [See also 11A55, 40A15]
[xref: 11A55, 40A15]
| 30B99 |
None of the above, but in this section
| |
30Cxx
| Geometric function theory
| 30C10 |
Polynomials
| 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}
[xref: 26C10]
| 30C20 |
Conformal mappings of special domains
| 30C25 |
Covering theorems in conformal mapping theory
| 30C30 |
Numerical methods in conformal mapping theory [See also 65E05]
| 30C35 |
General theory of conformal mappings
| 30C40 |
Kernel functions and applications
| 30C45 |
Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
| 30C50 |
Coefficient problems for univalent and multivalent functions
| 30C55 |
General theory of univalent and multivalent functions
| 30C62 |
Quasiconformal mappings in the plane
| 30C65 |
Quasiconformal mappings in $R^n$, other generalizations
| 30C70 |
Extremal problems for conformal and quasiconformal mappings, variational methods
| 30C75 |
Extremal problems for conformal and quasiconformal mappings, other methods
| 30C80 |
Maximum principle; Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination
| 30C85 |
Capacity and harmonic measure in the complex plane [See also 31A15]
[xref: 31A15]
| 30C99 |
None of the above, but in this section
| |
30Dxx
| Entire and meromorphic functions, and related topics
[xref: 34Mxx]
| 30D05 |
Functional equations in the complex domain, iteration and composition of analytic functions [See also 34Mxx, 37Fxx, 39-XX]
[xref: 37Fxx, 39B12, 39B32, 39Bxx]
| 30D10 |
Representations of entire functions by series and integrals
| 30D15 |
Special classes of entire functions and growth estimates
| 30D20 |
Entire functions, general theory
| 30D30 |
Meromorphic functions, general theory
| 30D35 |
Distribution of values, Nevanlinna theory
| 30D40 |
Cluster sets, prime ends, boundary behavior
[xref: 46F20]
| 30D45 |
Bloch functions, normal functions, normal families
| 30D50 |
Blaschke products, bounded mean oscillation, bounded characteristic, bounded functions, functions with positive real part
| 30D55 |
${H}^p$-classes
[xref: 46J15]
| 30D60 |
Quasi-analytic and other classes of functions
| 30D99 |
None of the above, but in this section
| |
30Exx
| Miscellaneous topics of analysis in the complex domain
[xref: 45Exx]
| 30E05 |
Moment problems, interpolation problems
[xref: 47A57]
| 30E10 |
Approximation in the complex domain
| 30E15 |
Asymptotic representations in the complex domain
[xref: 41A60]
| 30E20 |
Integration, integrals of Cauchy type, integral representations of analytic functions [See also 45Exx]
[xref: 45Exx]
| 30E25 |
Boundary value problems [See also 45Exx]
[xref: 35Q15, 45Exx, 46F20]
| 30E99 |
None of the above, but in this section
| |
30Fxx
| Riemann surfaces
[xref: 14H55, 32G15]
| 30F10 |
Compact Riemann surfaces and uniformization [See also 14H15, 32G15]
[xref: 14H15]
| 30F15 |
Harmonic functions on Riemann surfaces
| 30F20 |
Classification theory of Riemann surfaces
| 30F25 |
Ideal boundary theory
| 30F30 |
Differentials on Riemann surfaces
| 30F35 |
Fuchsian groups and automorphic functions [See also 11Fxx, 20H10, 22E40, 32Gxx, 32Nxx]
[xref: 11Fxx, 20H10, 32Nxx]
| 30F40 |
Kleinian groups [See also 20H10]
| 30F45 |
Conformal metrics (hyperbolic, Poincaré, distance functions)
| 30F50 |
Klein surfaces
| 30F60 |
Teichmüller theory [See also 32G15]
| 30F99 |
None of the above, but in this section
| |
30Gxx
| Generalized function theory
| 30G06 |
Non-Archimedean function theory [See also 12J25]; nonstandard function theory [See also 03H05]
[xref: 03H05, 12J25]
| 30G12 |
Finely holomorphic functions and topological function theory
| 30G20 |
Generalizations of Bers or Vekua type (pseudoanalytic, $p$-analytic, etc.)
| 30G25 |
Discrete analytic functions
| 30G30 |
Other generalizations of analytic functions (including abstract-valued functions)
| 30G35 |
Functions of hypercomplex variables and generalized variables
| 30G99 |
None of the above, but in this section
| |
30H05
| Spaces and algebras of analytic functions [See also 32A38, 46Exx, 46J15]
[xref: 32A38, 46Exx, 46J15]
| |