9.5 Applications in Analysis and Topology
Applications of advanced set theory to analysis and topology, including regularity properties, Banach spaces, measure theory, and topological classification.
Tag
Analysis
21 notes
58. Global Analysis, Analysis on Manifolds
This volume studies analysis on manifolds, combining differential geometry, functional analysis, and partial differential equations.
49. Calculus of Variations and Optimal Control; Optimization
This volume studies optimization of functionals and systems.
47. Operator Theory
This volume studies linear operators on Banach and Hilbert spaces, with emphasis on spectral properties, structure, and applications in analysis and...
46. Functional Analysis
This volume studies infinite-dimensional vector spaces and linear operators.
45. Integral Equations
This volume studies equations where the unknown function appears under an integral.
44. Integral Transforms, Operational Calculus
This volume studies integral transforms as tools for solving equations, analyzing signals, and transforming problems into more tractable forms.
43. Abstract Harmonic Analysis
This volume extends harmonic analysis to general locally compact groups.
42. Harmonic Analysis
This volume studies representation of functions via oscillatory components such as Fourier series and transforms.
41. Approximations and Expansions
This volume studies approximation of functions and data by simpler objects such as polynomials, splines, and rational functions.
40. Sequences, Series, Summability
This volume studies convergence, divergence, and summation methods for sequences and series.
39. Difference and Functional Equations
This volume studies equations defined by discrete steps and functional relations.
37. Dynamical Systems and Ergodic Theory
This volume studies systems that evolve over time, focusing on long-term behavior, stability, and statistical properties.
35. Partial Differential Equations
This volume studies equations involving partial derivatives of functions in several variables.
34. Ordinary Differential Equations
This volume studies differential equations involving functions of a single variable.
33. Special Functions
This volume studies classical and modern special functions arising as solutions to differential equations, integral transforms, and representation...
32. Several Complex Variables and Analytic Spaces
This volume studies functions of several complex variables, complex manifolds, and analytic spaces.
31. Potential Theory
This volume studies harmonic, subharmonic, and superharmonic functions, along with potentials and their applications to analysis, geometry, and...
30. Complex Analysis
This volume studies functions of a complex variable.
28. Measure and Integration
This volume develops measure theory and integration in a general setting.
26. Real Functions
This volume studies functions of real variables with an emphasis on limits, continuity, differentiation, integration, and fine properties of...