In mathematics, a positive-definite function is, depending on the context, either of two types of function. Let R {\displaystyle \mathbb {R} } be the set...

positive-definite. See, in particular: Positive-definite bilinear form Positive-definite function Positive-definite function on a group Positive-definite functional...

operator theory, a branch of mathematics, a positive-definite kernel is a generalization of a positive-definite function or a positive-definite matrix. It was...

operator theory, a positive-definite function on a group relates the notions of positivity, in the context of Hilbert spaces, and algebraic groups. It can be...

continuous positive-definite function on a locally compact abelian group corresponds to a finite positive measure on the Pontryagin dual group. The case...

\Gamma (n)=(n-1)!\,.} The gamma function can be defined via a convergent improper integral for complex numbers with positive real part: Γ ( z ) = ∫ 0 ∞ t...

mathematics, a zonal spherical function or often just spherical function is a function on a locally compact group G with compact subgroup K (often a maximal...

algebra of the Lie group of all positive real numbers under multiplication, the ordinary exponential function for real arguments is a special case of the...

matrices with the positive elements being the positive-definite matrices. The trace function defined on this C*-algebra is a positive functional, as the...

mathematics, a Siegel theta series is a Siegel modular form associated to a positive definite lattice, generalizing the 1-variable theta function of a lattice...

Analogues of several special functions have been defined on the space of positive definite matrices, among them the power function which goes back to Atle...

theta functions when dealing with the heat equation is that "a theta function is a special function that describes the evolution of temperature on a segment...

geometrically, there is only one positive definite real quadratic form of every dimension. Its isometry group is a compact orthogonal group O(n). This stands in contrast...

sufficient to ask that, for every continuous positive-definite compactly supported function f on G, the function Δ–1⁄2f has non-negative integral with respect...

of calculus relates definite integration to differentiation and provides a method to compute the definite integral of a function when its antiderivative...

solution to a definite integral ∫ a b f ( x ) d x {\displaystyle \int _{a}^{b}f(x)\,dx} to a given degree of accuracy. If f(x) is a smooth function integrated...

a single variable. It can variously be expressed in the form of a definite integral, a trigonometric series, and various other forms. It is intimately...

In mathematics, the E8 lattice is a special lattice in R8. It can be characterized as the unique positive-definite, even, unimodular lattice of rank 8...

general, the roots of a polynomial of degree five or higher cannot be expressed in terms of nth roots. If A is a positive-definite matrix or operator, then...

H_{j}\rangle \right)\rangle } This matrix is positive semi-definite, and may be interpreted as a metric tensor, specifically, a Riemannian metric. Equipping the space...

theorem Plancherel's theorem Convolution Convolution theorem Positive-definite function Poisson summation formula Paley-Wiener theorem Sobolev space Time–frequency...

a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common symbols for a wave...

{\hbar }{2}}} apply. It is clear that since the plane wave has definite momentum (definite energy), the probability of finding the particle's location is...

In mathematics, the Lambert W function, also called the omega function or product logarithm, is a multivalued function, namely the branches of the converse...

meanings to the noun phrase, such as definiteness, proximity, number, and the like.: 115  While the determinative function is typically realized by determiner...

operator-valued positive-definite function arises in this way. Recall that every (continuous) scalar-valued positive-definite function on a topological group induces...

vector b (component-wise inequality). As a special case when Q is symmetric positive-definite, the cost function reduces to least squares: where Q = RTR...

"separate" a subset MΦ from a previously formed set M: "AXIOM III. (Axiom of separation). Whenever the propositional function Φ(x) is definite for all elements...

and/or large problems. When f {\displaystyle f} is a convex quadratic function with positive-definite Hessian B {\displaystyle B} , one would expect the...

and Im,n constructions, respectively. The theta function of a unimodular positive definite lattice is a modular form whose weight is one half the rank...