The Malgrange preparation theorem is a result in complex analysis and algebraic geometry that is concerned with the behavior of analytic functions and their singularities. It provides a way to analyze and decompose certain classes of analytic functions near isolated singular points.

The Lagrange reversion theorem is a result in mathematical analysis and combinatorics that relates to the coefficients of a power series. More specifically, it provides a method to express the coefficients of the inverse of a power series in terms of the coefficients of the original series.

Krein's condition refers to a specific criterion used in the mathematical field of functional analysis, particularly in the study of operators on Hilbert spaces. It is particularly associated with the stability of operators and the spectral properties of certain classes of linear operators, especially in the context of self-adjoint operators. In its most well-known form, Krein's condition provides a way to characterize the stability of a linear operator with respect to perturbations.

Komlós' theorem, also known as Komlós' conjecture, is a result in combinatorial mathematics, specifically in the field of graph theory. The theorem deals with the concept of almost perfect matchings in large graphs.

Kneser's theorem is a result in the theory of differential equations, particularly in the context of linear differential equations with variable coefficients. It addresses the behavior of solutions for higher-order linear ordinary differential equations.

The Khintchine inequality is a result in mathematical analysis, particularly in the study of probability theory and functional analysis. It pertains to the properties of sums of independent random variables, specifically regarding their expected values and moments.

The Kantorovich inequality is a result in the realm of functional analysis, specifically associated with the theory of measures and integrable functions. It provides a crucial estimate related to the norms of integral operators defined on vector spaces of measurable functions. In one of its common forms, the Kantorovich inequality relates to the notion of integrable functions and their norms.

Jensen's inequality is a fundamental result in convex analysis and probability theory that relates to convex functions.

Integration using Euler's formula involves the application of Euler's formula to express complex exponentials in terms of sine and cosine functions, which can simplify the integration of certain functions, especially those involving trigonometric terms.

Holmgren's uniqueness theorem is a result in the theory of partial differential equations (PDEs), particularly concerning elliptic equations. It addresses the uniqueness of solutions to certain boundary value problems.

Helly's selection theorem is a result in combinatorial geometry and convex analysis, named after the mathematician Eduard Helly. The theorem asserts conditions under which a family of convex sets possesses a point in common, based on the intersections of smaller subfamilies of those sets. The precise statement of Helly's selection theorem typically involves a finite collection of convex sets in \(\mathbb{R}^d\).

The Goldbach–Euler theorem is a result in number theory that relates to the representation of even integers as sums of prime numbers. More specifically, it builds on the ideas of the original Goldbach conjecture. While the conjecture itself states that every even integer greater than 2 can be expressed as the sum of two prime numbers, the Goldbach–Euler theorem provides a more generalized framework.

Godunov's theorem is a result in the field of numerical analysis, specifically related to the numerical solution of hyperbolic partial differential equations (PDEs). It is named after the Russian mathematician S. K. Godunov, who contributed significantly to the development of finite volume methods for solving these types of equations.

Glaeser's continuity theorem is a result in the field of real analysis, specifically concerning the continuity properties of certain functions. While I cannot provide the specific wording of the theorem, I can summarize its significance and implications. The theorem is often related to the concepts of continuity in functions defined on certain spaces. It typically deals with the conditions under which a function can be approximated continuously by other functions, or under which certain limits exist as parameters change.

The Gaussian integral refers to the integral of the function \( e^{-x^2} \) over the entire real line.

Fuchs' theorem is a result in the field of complex analysis, particularly in the study of ordinary differential equations with singularities. The theorem provides conditions under which a linear ordinary differential equation with an irregular singular point can be solved using power series methods. Specifically, Fuchs' theorem states that if a linear differential equation has only regular singular points, then around each regular singular point, there exist solutions that can be expressed as a Frobenius series.

The Fraňková–Helly selection theorem is a result in the field of functional analysis and topology, specifically concerning the selection of points from family of sets. It builds upon the classical Helly's theorem, which deals with finite intersections of convex sets in Euclidean spaces. The Fraňková–Helly selection theorem provides conditions under which one can extract a sequence from a family of sets that converges in a certain sense.

The Fenchel–Moreau theorem is a fundamental result in convex analysis that relates the concepts of convex conjugates and duality. It characterizes the relationship between a convex function and its conjugate. Let \( f : \mathbb{R}^n \to \mathbb{R} \) be a proper, convex, and lower semicontinuous function.

Fenchel's duality theorem is a fundamental result in convex analysis and optimization, which establishes a relationship between a convex optimization problem and its dual problem. Specifically, it provides conditions under which the solution of a primal convex optimization problem can be found by solving its dual.

The Dirichlet–Jordan test is a criterion used in analysis, particularly in the study of the convergence of series of functions, such as Fourier series. The test is useful for determining the pointwise convergence of a series of functions, especially when dealing with orthogonal functions or trigonometric series.