Approximations by the Cauchy-type integrals with piecewise linear densities
نویسندگان
چکیده
منابع مشابه
a cauchy-schwarz type inequality for fuzzy integrals
نامساوی کوشی-شوارتز در حالت کلاسیک در فضای اندازه فازی برقرار نمی باشد اما با اعمال شرط هایی در مسئله مانند یکنوا بودن توابع و قرار گرفتن در بازه صفر ویک می توان دو نوع نامساوی کوشی-شوارتز را در فضای اندازه فازی اثبات نمود.
15 صفحه اولConvergence Results for Piecewise Linear Quadratures for Cauchy Principal Value Integrals
Conditions on 7c and / are given for the pointwise and uniform convergence to the Cauchy principal value integral rmm _1<A<1, j-i x~x of a sequence of integrals of piecewise linear approximations to f(x) or g\(x) = (f(x) — f(X))/(x — A). The important special case, k(x) = (1 a;)a(l + x)13, is considered in detail.
متن کاملBoundary Values of Cauchy Type Integrals
Results by A. G. Poltoratskĭı and A. B. Aleksandrov about nontangential boundary values of pseudocontinuable H2-functions on sets of zero Lebesgue measure are used for the study of operators on L2-spaces on the unit circle. For an arbitrary bounded operator X acting from one such L2-space to another and having the property that the commutator of it with multiplication by the independent variabl...
متن کاملInvertible Piecewise Linear Approximations for Color Reproduction
We consider the use of linear splines with variable knots for the approximation of unknown functions from data , motivated by control and estimation problems arising in color systems management. Unlike most popular nonlinear-in-parameters representations, piecewise linear (PL) functions can be simply inverted in closed form. For the one-dimensional case, we present a study comparing P L and neu...
متن کاملPiecewise-Linear Approximations of Uncertain Functions
We study the problem of approximating a function F : R→ R by a piecewise-linear function F when the values of F at {x1, . . . , xn} are given by a discrete probability distribution. Thus, for each xi we are given a discrete set yi,1, . . . , yi,mi of possible function values with associated probabilities pi,j such that Pr[F(xi) = yi,j ] = pi,j . We define the error of F as error(F,F) = maxi=1 E...
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: Applications of Mathematics
سال: 2012
ISSN: 0862-7940,1572-9109
DOI: 10.1007/s10492-012-0038-3