Kharitonov's theorem is a result in control theory, particularly in the study of linear time-invariant (LTI) systems and the stability of polynomial systems. It is often used in the analysis of systems with polynomials that have parameters, allowing for the examination of how variations in those parameters affect stability. The theorem provides a method to determine the stability of a family of linear systems defined by a parameterized characteristic polynomial.

Fejér's theorem is a result in the theory of Fourier series, specifically concerning the convergence of the Fourier series of a periodic function. It states that if \( f \) is a piecewise continuous function on the interval \([-L, L]\), then the sequence of partial sums of its Fourier series converges uniformly to the average of the left-hand and right-hand limits of \( f \) at each point.

Chebotarev's theorem is a result in number theory that deals with the distribution of roots of unity in relation to polynomial equations over finite fields. Specifically, it is often associated with the density of certain classes of primes in number fields, but it can be stated in a context relevant to roots of unity.

The Routh–Hurwitz theorem is a mathematical criterion used in control theory and stability analysis of linear time-invariant (LTI) systems. It provides a systematic way to determine whether all roots of a given polynomial have negative real parts, which indicates that the system is stable.

Wirtinger's representation theorem and projection theorem are fundamental results in mathematical analysis, particularly in the fields of functional analysis and the theory of Sobolev spaces. They are often applied in the study of harmonic functions, the solution of partial differential equations, and variational problems. ### Wirtinger's Representation Theorem: The Wirtinger representation theorem provides a way to connect the Dirichlet energy of functions to their boundary conditions.

The AF + BG theorem is a concept in the field of mathematics, specifically in the area of set theory and topology. However, the notation AF + BG does not correspond to a widely recognized theorem or principle within standard mathematical literature or education. It's possible that this notation is specific to a certain context, course, or area of research that is not broadly covered.

Blum's speedup theorem is a result in the field of computational complexity theory, specifically dealing with the relationship between the time complexity of algorithms and the computation of functions. Formulated by Manuel Blum in the 1960s, the theorem essentially asserts that if a certain function can be computed by a deterministic Turing machine within a certain time bound, then there exists an alternative algorithm (or Turing machine) that computes the same function more quickly.

Algebraic number theory is a branch of mathematics that studies the properties of numbers and the relationships between them, particularly through the lens of algebraic structures such as rings, fields, and ideals. Within this field, theorems often address the properties of algebraic integers, the structure of algebraic number fields, and the behavior of various arithmetic objects.

The Friedlander–Iwaniec theorem is a result in number theory, specifically in the area of additive number theory concerning the distribution of prime numbers. It was established by the mathematicians J. Friedlander and H. Iwaniec in the early 1990s.

The Kronecker limit formula is an important result in the theory of modular forms and number theory. It relates the behavior of certain L-functions to the special values of those functions at integers. Specifically, it provides a way to compute the special value of an L-function associated with a point on a certain modular curve. The formula can be stated in the context of the Dedekind eta function and the Eisenstein series.

The Landsberg–Schaar relation is a concept in the field of thermodynamics, particularly in relation to the thermoelectric properties of materials. It establishes a relationship between the electrical conductivity, the Seebeck coefficient, and the thermal conductivity of a material. This relation is significant because it helps to optimize materials for thermoelectric applications, such as in power generation or cooling devices.

Abhyankar's conjecture, proposed by the mathematician Shreeram S. Abhyankar in the 1960s, is a conjecture in the field of algebraic geometry, specifically related to the theory of algebraic surfaces and their rational points. The conjecture primarily deals with the growth of the functions associated with the algebraic curves defined over algebraically closed fields and involves questions about the intersections and the number of points of these curves.

Abhyankar's lemma is a result in the area of algebraic geometry, specifically dealing with the properties of algebraic varieties and their points over fields. Named after the mathematician Shivaramakrishna Abhyankar, the lemma provides a criterion for the existence of certain types of points in the context of algebraic varieties defined over a field.

The Dimension Theorem for vector spaces is a fundamental result in linear algebra that relates the dimensions of certain components of vector spaces and their subspaces.

The Dold–Kan correspondence is a fundamental theorem in algebraic topology and homological algebra that establishes a relationship between two important categories: the category of simplicial sets and the category of chain complexes of abelian groups (or modules). It is named after mathematicians Alfred Dold and D. K. Kan, who formulated it in the context of homotopy theory.

The Fundamental Lemma is a key result in the Langlands program, which is a vast and influential set of conjectures and theories in number theory and representation theory that seeks to relate Galois groups and automorphic forms. The Langlands program is named after Robert P. Langlands, who initiated these ideas in the late 1960s.

The Fundamental Theorem on Homomorphisms, often referred to in the context of group theory or algebra in general, states that there is a specific relationship between a group, a normal subgroup, and the quotient group formed by the subgroup. In summary, it describes how to relate the structure of a group to its quotient by a normal subgroup.

The Latimer–MacDuffee theorem is a result in the field of algebra, specifically concerning finite abelian groups and their decompositions. It states that any finite abelian group can be expressed as a direct sum of cyclic groups, and the number of different ways to express a finite abelian group as such a direct sum is given by a specific combinatorial expression related to its invariant factors.

The Primitive Element Theorem is a fundamental result in field theory, which deals with field extensions in algebra.

The Quillen–Suslin theorem, also known as the vanishing of the topological K-theory of the field of rational numbers, is a fundamental result in algebraic topology and the theory of vector bundles. It states that every vector bundle over a contractible space is trivial. More specifically, it can be expressed in the context of finite-dimensional vector bundles over real or complex spaces.