Named Analytic Theorems & Operators¶

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Abstractions that are named theorems, operators, or invariants from mathematical analysis and geometry, including convergence and continuity results such as Egorov's theorem and the Weierstrass M-test, functional-analytic operators like densely defined operators and functional determinants, and dynamical or geometric quantities such as heteroclinic orbits and filling radius.

39 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

Absolute value — In mathematics, the absolute value or modulus of a real number x , is the (non-negative) magnitude measured without regard to its sign.
Abstract additive Schwarz method — In mathematics, the abstract additive Schwarz method, named after Hermann Schwarz, is an abstract version of the additive Schwarz method for boundary value problems on partial differential equations, formulated only in terms of linear algebra without reference to domains, subdomains, etc.
Andreotti–Norguet Formula — The Andreotti–Norguet formula, first introduced by , is a higher–dimensional analogue of Cauchy integral formula for expressing the derivatives of a holomorphic function.
Bernstein's theorem (approximation theory) — In approximation theory, Bernstein's theorem is a converse to Jackson's theorem.
Big O in probability notation — The order in probability notation is used in probability theory and statistical theory in direct parallel to the big O notation that is standard in mathematics.
Coarea formula — For smooth functions the formula is a result in multivariate calculus which follows from a change of variables.
Coinduction — In computer science, coinduction is a technique for defining and proving properties of systems of concurrent interacting objects.
Céa's lemma — Céa's lemma bounds the error of a Galerkin finite-element approximation by a continuity-to-coercivity constant times the best approximation error available in the chosen subspace.
Densely defined operator — In mathematics – specifically, in operator theory – a densely defined operator or partially defined operator is a type of partially defined function.
Egorov's theorem — It is also named Severini–Egoroff theorem or Severini–Egorov theorem, after Carlo Severini, an Italian mathematician, and Dmitri Egorov, a Russian mathematician and geometer, who published independent proofs respectively in 1910 and 1911.
Filling radius — In Riemannian geometry, the filling radius of a Riemannian manifold X is a metric invariant of X.
Fractional calculus — Fractional calculus is a branch of mathematical analysis that studies the several different possibilities of defining real number powers or complex number powers of the differentiation operator D.
Functional determinant — The corresponding quantity det(S) is called the functional determinant of S.
Hafnian — In mathematics, the hafnian is a scalar function of a symmetric matrix that generalizes the permanent.
Helffer–Sjöstrand Formula — The Helffer–Sjöstrand formula is a mathematical tool used in spectral theory and functional analysis to represent functions of self-adjoint operators.
Heteroclinic orbit — In mathematics, in the phase portrait of a dynamical system, a heteroclinic orbit (sometimes called a heteroclinic connection) is a path in phase space which joins two different equilibrium points.
Inaccessible cardinal — A strongly inaccessible cardinal is an uncountable regular strong-limit cardinal; in modern usage, the unqualified term inaccessible cardinal normally denotes this strong form.
Isothermal coordinates — In mathematics, specifically in differential geometry, isothermal coordinates on a Riemannian manifold are local coordinates where the metric is conformal to the Euclidean metric.
Kirkwood approximation — The Kirkwood approximation for a discrete probability density function P(x_{1},x_{2},\ldots ,x_{n}) is given by.
Large deviations theory — Thus to estimate the premium you have to ask the following question: "What should we choose as the premium q such that over N months the total claim C = \Sigma X_i should be less than This is clearly the same question asked by the large deviations theory.
Lefschetz zeta function — In mathematics, the Lefschetz zeta-function is a tool used in topological periodic and fixed point theory, and dynamical systems.
Lie group — In mathematics, a Lie group (pronounced ) is a group that is also a differentiable manifold, such that group multiplication and taking inverses are both differentiable.
Lipschitz continuity — In mathematical analysis, Lipschitz continuity is a regularity property of functions between metric spaces that is stronger than uniform continuity, and hence also stronger than continuity.
Lévy's modulus of continuity theorem — Lévy's modulus of continuity theorem is a theorem that gives a result about an almost sure behaviour of an estimate of the modulus of continuity for Wiener process, that is used to model what's known as Brownian motion.
Mean Value Theorem — In calculus and real analysis, the mean value theorem (or Lagrange's mean value theorem) is a theorem about differentiable functions, roughly stating that the average rate of change of such a function over an interval is equal to the instantaneous rate of change at some point in the interval.
Mehler Kernel — The Mehler kernel is a complex-valued function found to be the propagator of the quantum harmonic oscillator.
Method of continued fractions — The method of continued fractions is a method developed specifically for solution of integral equations of quantum scattering theory like Lippmann–Schwinger equation or Faddeev equations.
Minakshisundaram–Pleijel zeta function — The Minakshisundaram–Pleijel zeta function is a zeta function encoding the eigenvalues of the Laplacian of a compact Riemannian manifold.
Orbital-Free Density Functional Theory — In computational chemistry, orbital-free density functional theory (OFDFT) is a quantum mechanical approach to electronic structure determination which is based on functionals of the electronic density.
p-Variation — In mathematical analysis, p-variation is a collection of seminorms on functions from an ordered set to a metric space, indexed by a real number p\geq 1 . p-variation is a measure of the regularity or smoothness of a function.
Parabolic Hausdorff dimension — In fractal geometry, the parabolic Hausdorff dimension is a restricted version of the genuine Hausdorff dimension.
Parallel (operator) — The parallel operator | (pronounced "parallel", following the parallel lines notation from geometry; also known as reduced sum, parallel sum or parallel addition) is a binary operation which is used as a shorthand in electrical engineering, but is also used in kinetics, fluid mechanics and financial mathematics.
Quotient rule — In calculus, the quotient rule is a method of finding the derivative of a function that is the ratio of two differentiable functions.
Riesz's lemma — In mathematics, Riesz's lemma (after Frigyes Riesz) is a lemma in functional analysis.
Spectral theory of compact operators — In functional analysis, compact operators are linear operators on Banach spaces that map bounded sets to relatively compact sets.
Terminal singularity — In particular, a terminal 3-fold singularity is the quotient of a hypersurface singularity with multiplicity 2 by a finite cyclic group.
Valuation (geometry) — In geometry, a valuation is a finitely additive function from a collection of subsets of a set X to an abelian semigroup.
Weierstrass M-Test — In mathematics, the Weierstrass M-test is a test for determining whether an infinite series of functions converges uniformly and absolutely.
Wilkie's theorem — In mathematics, Wilkie's theorem is a result by Alex Wilkie about the theory of ordered fields with an exponential function, or equivalently about the geometric nature of exponential varieties.