| 30-XX |
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Functions of a complex variable |
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30-00 |
General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to functions of a complex variable |
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30-01 |
Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functions of a complex variable |
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30-02 |
Research exposition (monographs, survey articles) pertaining to functions of a complex variable |
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30-03 |
History of functions of a complex variable [Consider also classification numbers from Section 01-XX] |
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30-04 |
Software, source code, etc. for problems pertaining to functions of a complex variable |
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30-06 |
Proceedings, conferences, collections, etc. pertaining to functions of a complex variable |
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30-08 |
Computational methods for problems pertaining to functions of a complex variable [See also 65Exx] |
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30-11 |
Research data for problems pertaining to functions of a complex variable |
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30A05 |
Monogenic and polygenic functions of one complex variable |
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30A10 |
Inequalities in the complex plane |
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30A99 |
None of the above, but in this section |
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30B10 |
Power series (including lacunary series) in one complex variable |
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30B20 |
Random power series in one complex variable |
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30B30 |
Boundary behavior of power series in one complex variable; over-convergence |
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30B40 |
Analytic continuation of functions of one complex variable |
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30B50 |
Dirichlet series, exponential series and other series in one complex variable [See also 11M41, 42-XX] |
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30B60 |
Completeness problems, closure of a system of functions of one complex variable |
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30B70 |
Continued fractions; complex-analytic aspects [See also 11A55, 40A15] |
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30B99 |
None of the above, but in this section |
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30C10 |
Polynomials and rational functions of one complex variable |
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30C15 |
Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) {For algebraic theory, see 12D10; for real methods, see 26C10} |
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30C20 |
Conformal mappings of special domains |
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30C25 |
Covering theorems in conformal mapping theory |
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30C30 |
Schwarz-Christoffel-type mappings [See also 65E10] |
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30C35 |
General theory of conformal mappings |
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30C40 |
Kernel functions in one complex variable and applications |
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30C45 |
Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) |
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30C50 |
Coefficient problems for univalent and multivalent functions of one complex variable |
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30C55 |
General theory of univalent and multivalent functions of one complex variable |
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30C62 |
Quasiconformal mappings in the complex plane |
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30C65 |
Quasiconformal mappings in $\mathbb{R}^n$, other generalizations |
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30C70 |
Extremal problems for conformal and quasiconformal mappings, variational methods |
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30C75 |
Extremal problems for conformal and quasiconformal mappings, other methods |
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30C80 |
Maximum principle, Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination |
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30C85 |
Capacity and harmonic measure in the complex plane [See also 31A15] |
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30C99 |
None of the above, but in this section |
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30D05 |
Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable [See also 34Mxx, 37Fxx, 39-XX] |
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30D10 |
Representations of entire functions of one complex variable by series and integrals |
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30D15 |
Special classes of entire functions of one complex variable and growth estimates |
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30D20 |
Entire functions of one complex variable (general theory) |
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30D30 |
Meromorphic functions of one complex variable (general theory) |
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30D35 |
Value distribution of meromorphic functions of one complex variable, Nevanlinna theory |
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30D40 |
Cluster sets, prime ends, boundary behavior |
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30D45 |
Normal functions of one complex variable, normal families |
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30D60 |
Quasi-analytic and other classes of functions of one complex variable |
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30D99 |
None of the above, but in this section |
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30E05 |
Moment problems and interpolation problems in the complex plane |
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30E10 |
Approximation in the complex plane |
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30E15 |
Asymptotic representations in the complex plane |
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30E20 |
Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane [See also 45Exx] |
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30E25 |
Boundary value problems in the complex plane [See also 45Exx] |
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30E99 |
None of the above, but in this section |
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30F10 |
Compact Riemann surfaces and uniformization [See also 14H15, 32G15] |
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30F15 |
Harmonic functions on Riemann surfaces |
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30F20 |
Classification theory of Riemann surfaces |
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30F25 |
Ideal boundary theory for Riemann surfaces |
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30F30 |
Differentials on Riemann surfaces |
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30F35 |
Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) [See also 11Fxx, 20H10, 22E40, 32Gxx, 32Nxx] |
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30F40 |
Kleinian groups (aspects of compact Riemann surfaces and uniformization) [See also 20H10] |
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30F45 |
Conformal metrics (hyperbolic, Poincaré, distance functions) |
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30F50 |
Klein surfaces |
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30F60 |
Teichmüller theory for Riemann surfaces [See also 32G15] |
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30F99 |
None of the above, but in this section |
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30G06 |
Non-Archimedean function theory [See also 12J25]; nonstandard function theory [See also 03H05] |
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30G12 |
Finely holomorphic functions and topological function theory |
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30G20 |
Generalizations of Bers and Vekua type (pseudoanalytic, $p$-analytic, etc.) |
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30G25 |
Discrete analytic functions |
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30G30 |
Other generalizations of analytic functions (including abstract-valued functions) |
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30G35 |
Functions of hypercomplex variables and generalized variables |
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30G99 |
None of the above, but in this section |
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30H05 |
Spaces of bounded analytic functions of one complex variable |
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30H10 |
Hardy spaces [See also 42B30, 46E30] |
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30H15 |
Nevanlinna spaces and Smirnov spaces |
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30H20 |
Bergman spaces and Fock spaces [See also 46E30, 46E35] |
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30H25 |
Besov spaces and $Q_p$-spaces |
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30H30 |
Bloch spaces |
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30H35 |
BMO-spaces |
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30H40 |
Zygmund spaces |
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30H45 |
de Branges-Rovnyak spaces |
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30H50 |
Algebras of analytic functions of one complex variable |
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30H80 |
Corona theorems |
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30H99 |
None of the above, but in this section |
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30J05 |
Inner functions of one complex variable |
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30J10 |
Blaschke products |
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30J15 |
Singular inner functions of one complex variable |
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30J99 |
None of the above, but in this section |
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30K05 |
Universal Taylor series in one complex variable |
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30K10 |
Universal Dirichlet series in one complex variable |
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30K15 |
Universal functions of one complex variable |
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30K20 |
Compositional universality |
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30K99 |
None of the above, but in this section |
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30L05 |
Geometric embeddings of metric spaces |
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30L10 |
Quasiconformal mappings in metric spaces |
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30L15 |
Inequalities in metric spaces |
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30L99 |
None of the above, but in this section |
