The term "Chicago School" in the context of mathematical analysis typically refers to a group of researchers affiliated with the University of Chicago who have made significant contributions to various areas of mathematics, particularly in analysis, probability, and other related fields. While the phrase is also commonly associated with economics (the Chicago School of Economics), in mathematics, it reflects a style of research and pedagogical approach that emphasizes rigor, intuition, and application.

The Chazy equation is a type of differential equation that is notable in the field of algebraic curves and modular forms. It is generally expressed in the context of elliptic functions and involves a third-order differential equation with specific properties.

The Carleson–Jacobs theorem is a result in harmonic analysis concerning the behavior of certain functions in terms of their boundedness properties and the behavior of their Fourier transforms. It is named after mathematicians Lennart Carleson and H.G. Jacobs. The theorem essentially addresses the relationship between certain types of singular integral operators and the boundedness of functions in various function spaces, including \( L^p \) spaces.

The Calogero–Degasperis–Fokas (CDF) equation is a nonlinear partial differential equation that arises in mathematical physics and integrable systems. It is named after mathematicians Francesco Calogero, Carlo Degasperis, and Vassilis Fokas.

FBSP (Fast Biorthogonal Spline Wavelet) is a type of wavelet that is part of the broader family of biorthogonal wavelets. Biorthogonal wavelets are characterized by having two sets of wavelet functions: one set for analysis (decomposition) and another set for synthesis (reconstruction).

The Favard operator is an integral operator used in the field of functional analysis and approximation theory. It is typically associated with the approximation of functions and the study of convergence properties in various function spaces. The operator is used to construct a sequence of polynomials that can approximate continuous functions, particularly in the context of orthogonal polynomials. The Favard operator can be defined in a way that it maps continuous functions to sequences or series of polynomials by integrating against a certain measure.

The Favard constant is a mathematical constant associated with the study of certain types of geometric shapes and their properties, particularly in relation to the concept of area and measure in Euclidean space. It is named after the French mathematician Jean Favard. In the context of convex shapes in the plane, the Favard constant provides a way to express the relationship between the area of a convex set and the area of its symmetrized version.

The Bohr–Favard inequality is a result in analysis that applies to integrable functions. It is named after the mathematicians Niels Henrik Abel and Pierre Favard. The inequality concerns the behavior of functions and their integrals, particularly in the context of convex functions and the properties of the Lebesgue integral.

The Cagniard–De Hoop method is a mathematical technique used in seismology and acoustics for solving wave propagation problems, particularly in the context of wave equations. It is especially useful for analyzing wavefields generated by a point source in a medium.

The Burkill integral is a mathematical concept that is part of the theory of integration, particularly in the context of functional analysis and the study of measures. Named after the British mathematician William Burkill, the Burkill integral extends the notion of integration to include more generalized types of functions and measures, particularly in the setting of Banach spaces.

The Bishop–Phelps theorem is a result in functional analysis that addresses the relationship between the norm of a continuous linear functional on a Banach space and the structure of the space itself. More specifically, it deals with the existence of points at which the functional attains its norm.

The Birkhoff–Kellogg invariant-direction theorem is a result in the field of topology and fixed-point theory, specifically in the study of continuous functions on convex sets. The theorem addresses the behavior of continuous functions defined on convex subsets of a Euclidean space.

The Bauer Maximum Principle is a concept in the field of functional analysis, particularly in the study of operators and matrices in Hilbert spaces. The principle is named after the mathematician Fritz Bauer. In essence, the Bauer Maximum Principle pertains to the spectral properties of bounded linear operators.

The Baskakov operator is a type of linear positive operator associated with the approximation of functions. It is named after the mathematician O. M. Baskakov, who introduced it as a means of approximating continuous functions on the interval \([0, 1]\). The Baskakov operator can be defined for a function \( f \) that is defined on the interval \([0, 1]\).

The term "Banach measure" is not a standard term in measure theory or functional analysis, but it might refer to several concepts that are associated with the work of mathematician Stefan Banach, especially concerning measures within vector spaces or more abstract settings. In a more specific context, "Banach measure" can refer to the concept of a measure defined on a Banach space, which is a complete normed vector space.

An analytic polyhedron is a geometric object in mathematics that combines the concepts of polyhedra with analytic properties. Specifically, an analytic polyhedron is defined in the context of real or complex spaces and is typically described using analytic functions. 1. **Polyhedron Definition**: A polyhedron is a three-dimensional geometric figure with flat polygonal faces, straight edges, and vertices. Each face of a polyhedron is a polygon, and the overall shape can be described using vertices and edges.

Analysis of partial differential equations (PDEs) is a branch of mathematics that focuses on the study and solutions of equations involving unknown functions of several variables and their partial derivatives. PDEs are fundamental in describing various physical phenomena such as heat conduction, fluid dynamics, electromagnetic fields, and wave propagation.

Alexandrov's theorem is a result in the field of differential geometry, specifically regarding the properties of convex polyhedra and surfaces. There are a few key aspects to Alexandrov's work, but one of the most notable results often associated with his name is related to the characterization of convex polyhedra in terms of their geometric properties.

The Agranovich–Dynin formula is a mathematical result in the field of partial differential equations, particularly in the study of the spectral properties of self-adjoint operators. It provides a way to relate the spectral analysis of certain operators to the behavior of solutions of the differential equations associated with those operators. The formula is particularly relevant in the context of boundary value problems, where it can be used to analyze the distribution of eigenvalues and the properties of the eigenfunctions of the associated differential operators.

Agmon's inequality is a result in the field of mathematical analysis and partial differential equations, particularly in the study of elliptic operators and solutions to certain types of differential equations. It provides a bound on the decay of solutions to elliptic equations, showing how solutions that are non-negative can decay at infinity.