# Category:Analysis

From Encyclopedia of Mathematics

- 26-XX Category:Real functions {See also 54C30}
- 28-XX Category:Measure and integration {For analysis on manifolds, see 58-XX}
- 30-XX Category:Functions of a complex variable {For analysis on manifolds, see 58-XX}
- 31-XX Category:Potential theory {For probabilistic potential theory, see 60J45}
- 32-XX Category:Several complex variables and analytic spaces {For infinite-dimensional holomorphy, see 46G20, 58B12}
- 33-XX Category:Special functions (33-XX deals with the properties of functions as functions) {For orthogonal functions, see 42Cxx; for aspects of combinatorics, see 05Axx; for number-theoretic aspects, see 11-XX; for representation theory, see 22Exx}
- 40-XX Category:Sequences, series, summability
- 41-XX Category:Approximations and expansions {For all approximation theory in the complex domain, see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numerical approximation, see 65Dxx}
- 42-XX Category:Harmonic analysis on Euclidean spaces
- 43-XX Category:Abstract harmonic analysis {For other analysis on topological and Lie groups, see 22Exx}
- 44-XX Category:Integral transforms, operational calculus {For fractional derivatives and integrals, see 26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. For numerical methods, see 65R10}
- 45-XX Category:Integral equations
- 46-XX Category:Functional analysis {For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx}
- 47-XX Category:Operator theory

(MSC2010 codes)

## Subcategories

This category has the following 14 subcategories, out of 14 total.

## Pages in category "Analysis"

The following 194 pages are in this category, out of 194 total.

### A

- Abel criterion
- Abel summation method
- Abel transformation
- Absolute continuity
- Absolutely continuous measures
- Absolutely convergent improper integral
- Absolutely convergent series
- Absolutely integrable function
- Additive class of sets
- Additivity
- Airy equation
- Algebra of sets
- Alternating series
- Analytic Borel space
- Analytic capacity
- Analytic function
- Approximate continuity
- Approximate derivative
- Approximate differentiability
- Approximate limit
- Arzelà variation
- Atom

### B

### C

- Cantor ternary function
- Carathéodory measure
- Casorati-Sokhotskii-Weierstrass theorem
- Cauchy criteria
- Cauchy integral theorem
- Cauchy kernel
- Cauchy sequence
- Cauchy test
- Cauchy-Riemann equations
- Cesàro summation methods
- Change of variables in an integral
- Chebyshev theorem
- Conditional convergence
- Continued fraction
- Continuity, modulus of
- Convergence in probability
- Convergence of measures
- Convexity, logarithmic
- Convolution transform
- Creation operators
- Cylinder functions

### D

- D'Alembert criterion (convergence of series)
- Darboux theorem
- De la Vallée-Poussin criterion
- Dedekind criterion (convergence of series)
- Defective value
- Density of a set
- Density topology
- Differentiation of measures
- Dini criterion
- Dini-Lipschitz criterion
- Dirichlet criterion (convergence of series)
- Divergence theorem
- Du Bois-Reymond criterion (convergence of series)

### E

### F

### H

### I

### J

### L

- Lacunary sequence
- Lagrange function
- Lagrange multipliers
- Lambert summation method
- Lebesgue criterion
- Lebesgue decomposition
- Lebesgue integral
- Lebesgue point
- Leibniz criterion
- Leibniz rule
- Leibniz series
- Lipschitz condition
- Lipschitz constant
- Lipschitz function
- Lobachevskii criterion (for convergence)
- Local normal forms for dynamical systems
- Logarithmic convergence criterion
- Luzin-Privalov theorems

### M

### P

### R

### S

### T

**How to Cite This Entry:**

Analysis.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Analysis&oldid=20689