holomorphic representation

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• Holomorphic functional calculus — In mathematics, holomorphic functional calculus is functional calculus with holomorphic functions. That is to say, given a holomorphic function fnof; of a complex argument z and an operator T , the aim is to construct an operator:f(T),which in a… …   Wikipedia

• Theta representation — In mathematics, the theta representation is a particular representation of the Heisenberg group of quantum mechanics. It gains its name from the fact that the Jacobi theta function is invariant under the action of a discrete subgroup of the… …   Wikipedia

• Discrete series representation — In mathematics, a discrete series representation is an irreducible unitary representation of a locally compact topological group G that is a subrepresentation of the left regular representation of G on L²(G). In the Plancherel measure, such… …   Wikipedia

• Cuspidal representation — In number theory, cuspidal representations are certain representations of algebraic groups that occur discretely in L2 spaces. The term cuspidal is derived, at a certain distance, from the cusp forms of classical modular form theory. In the… …   Wikipedia

• Prehomogeneous vector space — In mathematics, a prehomogeneous vector space (PVS) is a finite dimensional vector space V together with a subgroup G of GL( V ) such that G has an open dense orbit in V . Prehomogeneous vector spaces were introduced by Mikio Sato in 1970 and… …   Wikipedia

• Hilbert space — For the Hilbert space filling curve, see Hilbert curve. Hilbert spaces can be used to study the harmonics of vibrating strings. The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It… …   Wikipedia

• Complex number — A complex number can be visually represented as a pair of numbers forming a vector on a diagram called an Argand diagram, representing the complex plane. Re is the real axis, Im is the imaginary axis, and i is the square root of –1. A complex… …   Wikipedia

• Borel–Weil theorem — In mathematics in the field of representation theory of compact Lie groups, the Borel–Weil theorem provides a concrete model for the irreducible representations as holomorphic sections of certain complex line bundles. It can be considered as a… …   Wikipedia

• Modular form — In mathematics, a modular form is a (complex) analytic function on the upper half plane satisfying a certain kind of functional equation and growth condition. The theory of modular forms therefore belongs to complex analysis but the main… …   Wikipedia

• Hardy space — In complex analysis, the Hardy spaces (or Hardy classes) Hp are certain spaces of holomorphic functions on the unit disk or upper half plane. They were introduced by Frigyes Riesz (Riesz 1923), who named them after G. H. Hardy, because of the… …   Wikipedia

• Complex plane — Geometric representation of z and its conjugate in the complex plane. The distance along the light blue line from the origin to the point z is the modulus or absolute value of z. The angle φ is the argument of z. In mathematics …   Wikipedia