On Pointwise Estimates of Positive Definite Functions With Given Support
نویسندگان
چکیده
منابع مشابه
On pointwise estimates of positive definite functions with given support
The following problem originated from a question due to Paul Turán. Suppose Ω is a convex body in Euclidean space R or in T, which is symmetric about the origin. Over all positive definite functions supported in Ω, and with normalized value 1 at the origin, what is the largest possible value of their integral? From this Arestov, Berdysheva and Berens arrived to pose the analogous pointwise extr...
متن کاملPointwise Estimates Formultivariate Interpolation Using Conditionally Positive Definite Functions
We seek pointwise error estimates for interpolants, on scattered data, constructed using a basis of conditionally positive deenite functions of order m, and polynomials of degree not exceeding m-1. Two diierent approaches to the analysis of such interpolation are considered. The former uses distributions and reproducing kernel ideas, whilst the latter is based on a Lagrange function approach. E...
متن کاملConvolution Roots of Radial Positive Definite Functions with Compact Support
A classical theorem of Boas, Kac, and Krein states that a characteristic function φ with φ(x) = 0 for |x| ≥ τ admits a representation of the form φ(x) = ∫ u(y)u(y + x) dy, x ∈ R, where the convolution root u ∈ L2(R) is complex-valued with u(x) = 0 for |x| ≥ τ/2. The result can be expressed equivalently as a factorization theorem for entire functions of finite exponential type. This paper examin...
متن کاملSome numerical radius inequalities with positive definite functions
Using several examples of positive definite functions, some inequalities for the numerical radius of matrices are investigated. Also, some open problems are stated.
متن کاملInterpolation with Positive Definite Functions
I t i s well-known t h a t k r i g i n g and i n t e r p o l a t i o n by s p l i n e s a r e e q u i v a l e n t . Kr ig ing i s based on a s t o c h a s t i c f o r m u l a t i o n whereas s p l i n e s a r e f o r m u l a t e d I n a d e t e r m i n i s t i c way. A t h i r d p r e s e n t a t i o n i s g i v e n i n terms of Rad ia l P a s i s F u n c t i o n s . The c n n n e c t l o n s 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: Canadian Journal of Mathematics
سال: 2006
ISSN: 0008-414X,1496-4279
DOI: 10.4153/cjm-2006-017-8