Harmonic functions on Hilbert space
نویسندگان
چکیده
منابع مشابه
Positive Definite Functions on Hilbert Space
is always non-negative, for any positive integer n and all points x1, . . . , xn in H is said to be positive definite on Hilbert space. In Schoenberg (1938), it was shown that a function is positive definite on Hilbert space if and only if it is completely monotonic, and this characterization is of central importance in the theory of radial basis functions and learning theory. In this paper, we...
متن کاملSome Harmonic Functions on Minkowski Space
This note presents elementary geometric descriptions of several simple families of harmonic functions on the upper sheet of the unit hyperboloid in Minkowski three-space. As is briefly discussed here, these calculations grew out of an earlier attempt to construct Poincaré series on punctured surfaces using Minkowski geometry. Introduction The material in this note grew out of an attempt (discus...
متن کاملMultipliers on a Hilbert Space of Functions on R
For a Hilbert space H ⊂ L loc (R) of functions on R we obtain a representation theorem for the multipliers M commuting with the shift operator S. This generalizes the classical result for multipliers in L(R) as well as our previous result for multipliers in weighted space L ω (R). Moreover, we obtain a description of the spectrum of S.
متن کاملLearning Positive Functions in a Hilbert Space
Semidefinite Programming Formulation By representer theorem: f(x) = ∑n l=1 αlK (Xi, x) under the condition that the function has an SoS representation, i.e., f(x) = φ(x)>Qφ(x) for some Q 0. Define a d × n matrix Φ = [φ(X1) · · ·φ(Xn)] and an n × n diagonal matrix A = diag(α) = diag(α1, . . . , αn). We have Q = ΦAΦ>. Q is d × d, but has rank n, which can be much smaller than d. The constraint on...
متن کاملOn uniformly bounded spherical functions in Hilbert space
Let G be a commutative group, written additively, with a neutral element 0, and let K be a finite group. Suppose that K acts on G via group automorphisms G 3 a 7→ ka ∈ G, k ∈ K. Let H be a complex Hilbert space and let L (H) be the algebra of all bounded linear operators on H. A mapping u : G→ L (H) is termed a K-spherical function if it satisfies (i) |K|−1 ∑ k∈K u(a+kb) = u(a)u(b) for any a, b...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 1972
ISSN: 0022-1236
DOI: 10.1016/0022-1236(72)90041-9