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INTERNATIONAL SCIENTIFIC-PROFESSIONAL CONFERENCE: "INCLUSIVE EDUCATION-STATUS AND CHALLENGES"
Goran PETRUSHEV
Journal of Special Education and Rehabilitation , 2012,
Abstract:
Traditional Bulgarian Hunter's Cuisine (Hunter's Cooking Book) (1939) [In Bulgarian]
A. Petrushev
Venets : The Belogradchik Journal for Local History, Cultural Heritage and Folk Studies , 2012,
Abstract: This very rare book was published in Belogradchik in 1939. The publisher is Stamen Kamenov. Stamen Kamenov owned a printing press, where several books of local and national importance were printed. This is a cookbook with recipes for cooking wild game. The book is relevant to modern man because it shows what has been the cuisine of old Bulgarians.
Decomposition of spaces of distributions induced by Hermite expansions
Pencho Petrushev,Yuan Xu
Mathematics , 2007,
Abstract: Decomposition systems with rapidly decaying elements (needlets) based on Hermite functions are introduced and explored. It is proved that the Triebel-Lizorkin and Besov spaces on $\R^d$ induced by Hermite expansions can be characterized in terms of the needlet coefficients. It is also shown that the Hermite Triebel-Lizorkin and Besov spaces are, in general, different from the respective classical spaces.
Heat kernel based decomposition of spaces of distributions in the framework of Dirichlet spaces
Gerard Kerkyacharian,Pencho Petrushev
Mathematics , 2012,
Abstract: Classical and non classical Besov and Triebel-Lizorkin spaces with complete range of indices are developed in the general setting of Dirichlet space with a doubling measure and local scale-invariant Poincar\'e inequality. This leads to Heat kernel with small time Gaussian bounds and H\"older continuity, which play a central role in this article. Frames with band limited elements of sub-exponential space localization are developed, and frame and heat kernel characterizations of Besov and Triebel-Lizorkin spaces are established. This theory, in particular, allows to develop Besov and Triebel-Lizorkin spaces and their frame and heat kernel characterization in the context of Lie groups, Riemannian manifold, and other settings.
Localized polynomial frames on the interval with Jacobi weights
Pencho Petrushev,Yuan Xu
Mathematics , 2005,
Abstract: As is well known the kernel of the orthogonal projector onto the polynomials of degree $n$ in $L^2(w_{\a,\b}, [-1, 1])$ with $w_{\a,\b}(t) = (1-t)^\a(1+t)^\b$ can be written in terms of Jacobi polynomials. It is shown that if the coefficients in this kernel are smoothed out by sampling a $C^\infty$ function then the resulting function has almost exponential (faster than any polynomial) rate of decay away from the main diagonal. This result is used for the construction of tight polynomial frames for $L^2(w_{\a,\b})$ with elements having almost exponential localization.
Localized polynomial frames on the ball
Pencho Petrushev,Yuan Xu
Mathematics , 2006,
Abstract: Almost exponentially localized polynomial kernels are constructed on the unit ball $B^d$ in $\RR^d$ with weights %functions $W_\mu(x)= (1-|x|^2)^{\mu-1/2}$, $\mu \ge 0$, by smoothing out the coefficients of the corresponding orthogonal projectors. These kernels are utilized to the design of cubature formulae on $B^d$ with respect to $W_\mu(x)$ and to the construction of polynomial tight frames in $L^2(B^d, W_\mu)$ (called needlets) whose elements have nearly exponential localization.
Nonlinear nonnested 2-D spline approximation
Martin Lind,Pencho Petrushev
Mathematics , 2015,
Abstract: Nonlinear approximation from regular piecewise polynomials (splines) of degree $
Sub-exponentially localized kernels and frames induced by orthogonal expansions
Kamen Ivanov,Pencho Petrushev,Yuan Xu
Mathematics , 2008,
Abstract: The aim of this paper is to construct sup-exponentially localized kernels and frames in the context of classical orthogonal expansions, namely, expansions in Jacobi polynomials, spherical harmonics, orthogonal polynomials on the ball and simplex, and Hermite and Laguerre functions.
Decomposition of spaces of distributions induced by tensor product bases
Kamen Ivanov,Pencho Petrushev,Yuan Xu
Mathematics , 2009,
Abstract: Rapidly decaying kernels and frames (needlets) in the context of tensor product Jacobi polynomials are developed based on several constructions of multivariate $C^\infty$ cutoff functions. These tools are further employed to the development of the theory of weighted Triebel-Lizorkin and Besov spaces on $[-1, 1]^d$. It is also shown how kernels induced by cross product bases can be constructed and utilized for the development of weighted spaces of distributions on products of multidimensional ball, cube, sphere or other domains.
Decomposition of weighted Triebel-Lizorkin and Besov spaces on the ball
G. Kyriazis,P. Petrushev,Yuan Xu
Mathematics , 2007,
Abstract: Weighted Triebel-Lizorkin and Besov spaces on the unit ball $B^d$ in $\Rd$ with weights $\W(x)= (1-|x|^2)^{\mu-1/2}$, $\mu \ge 0$, are introduced and explored. A decomposition scheme is developed in terms of almost exponentially localized polynomial elements (needlets) $\{\phi_\xi\}$, $\{\psi_\xi\}$ and it is shown that the membership of a distribution to the weighted Triebel-Lizorkin or Besov spaces can be determined by the size of the needlet coefficients $\{\ip{f,\phi_\xi}\}$ in appropriate sequence spaces.
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