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...

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

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...

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...

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...

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...

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...

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...

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...

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...

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...

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

{\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...

"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...

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

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

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...

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

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...

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

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...