|
30-XX
|
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
|
|
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]
|
|
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}
|
|
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 Rn, 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, Lindel\"of principle, analogues and generalizations; subordination
|
|
30C85
|
Capacity and harmonic measure in the complex plane
[See also
31A15]
|
|
30C99
|
None of the above, but in this section
|
|
30Dxx
|
Entire and meromorphic functions, and related topics
|
|
30D05
|
Functional equations in the complex domain, iteration and composition of analytic functions
[See also
34Mxx,
39-XX,
37Fxx]
|
|
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
|
|
30D45
|
Bloch functions, normal functions, normal families
|
|
30D50
|
Blaschke products, bounded mean oscillation, bounded characteristic, bounded functions, functions with positive real part
|
|
30D55
|
Hp-classes
|
|
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
|
|
30E05
|
Moment problems, interpolation problems
|
|
30E10
|
Approximation in the complex domain
|
|
30E15
|
Asymptotic representations in the complex domain
|
|
30E20
|
Integration, integrals of Cauchy type, integral representations of analytic functions
[See also
45Exx]
|
|
30E25
|
Boundary value problems
[See also
45Exx]
|
|
30E99
|
None of the above, but in this section
|
|
30Fxx
|
Riemann surfaces
|
|
30F10
|
Compact Riemann surfaces and uniformization
[See also
14H15,
32G15]
|
|
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]
|
|
30F40
|
Kleinian groups
[See also
20H10]
|
|
30F45
|
Conformal metrics (hyperbolic, Poincar\'e, distance functions)
|
|
30F50
|
Klein surfaces
|
|
30F60
|
Teichm\"uller 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]
|
|
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]
|