Results 131 to 140 of about 2,689 (164)

LOWER BOUNDS FOR THE DIRICHLET HEAT KERNEL

The Quarterly Journal of Mathematics, 1997
The paper considers the problem of finding a lower bound for the Dirichlet heat kernel \(K_D(t,x,y)\) of the semigroup \(\exp[t\Delta_D/2]\), where \(\Delta_D\) is the Dirichlet Laplacian of a proper, open and connected domain \(D\subset\mathbb{R}^n\). The author improves under some geometrical assumption some results of a lower bound for \(K_D(t,x,y)\)
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A GEOMETRIC CONSTRUCTION OF THE DIRICHLET KERNEL*

Transactions of the New York Academy of Sciences, 1974
AbstractIf sin (x/2) ≠ 0 then 1/2 + cos x + cos 2x + … + cos nx = sin (n + ½)x/2 sin (x/2). This relation is fundamental in the theory of Fourier series. We define a geometric construction in the euclidean plane whose analysis leads to this and related trigonometric identities.
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The integral modulus of continuity of the Dirichlet kernel and the conjugate Dirichlet kernel

Mathematical Notes, 1993
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Kernel and capacity estimates in Dirichlet spaces

Journal of Functional Analysis, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
El-Fallah, O., Elmadani, Y., Kellay, K.
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Dirichlet Heat Kernel Estimates for $��^{��/2}+ ��^{��/2}$

2009
For $d\geq 1$ and ...
Chen, Zhen-Qing, Kim, Panki, Song, Renming   +2 more
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On the best approximation of Dirichlet kernels

Mathematical Notes, 1993
The author uses the notations: \[ T_ n(x)= {a_ 0\over 2}+ \sum^ n_{k= 1} (a_ k \cos kx+ b_ k \sin kx);\quad D_ n(x)= {1\over 2}+ \sum^ n_{k=1} \cos kx, \] \[ \| T_ n\|_ L= {1\over \pi} \int^{2\pi}_ 0 | T_ n(x)| dx;\quad \| T_ n\|_ C= \max_ x | T_ n(x) |; \] \vskip2.0mm \[ C_ n= \sup\{\| T_ n\|_ C: \| T_ n\|_ L\leq 1\}; \] \[ \widetilde T_ n(x)= \sum ...
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Dirichlet Kernel. Pointwise and Uniform Convergence.

2017
The material of this chapter forms a central part of the theory of trigonometric Fourier series. In this chapter we will answer the following question: to what value does a trigonometric Fourier series converge?
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Half Dirichlet Problems and Decompositions of Poisson Kernels

Advances in Applied Clifford Algebras, 2007
Following the previous study on the unit ball of Delanghe et al, half-Dirichlet problems for the upper-half space are presented and solved. The solutions further lead to decompositions of the Poisson kernels, and the fact that the classical Dirichlet problems may be solved merely by using Cauchy transformation in the respective two contexts.
Richard Delanghe, Tao Qian
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Generalized weighted Bergman–Dirichlet and Bargmann–Dirichlet spaces: explicit formulae for reproducing kernels and asymptotics

Annals of Global Analysis and Geometry, 2015
The authors determine the reproducing kernels for certain weighted Bergman-Dirichlet spaces on the disk, denoted by \(\mathcal A_m^{2,\alpha}(\mathbb D_R)\), and their siblings on the plane, called by them weighted Bargmann-Dirichlet spaces. Here, \(\mathcal A_m^{2,\alpha}(\mathbb D_R)\) is the space of all holomorphic functions \(f\) on the disk ...
A. El Hamyani, A. Ghanmi, A. Intissar, Z. Mouhcine, M. Souid El Aïnin   +4 more
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Bayesian Folding-In with Dirichlet Kernels for PLSI

Seventh IEEE International Conference on Data Mining (ICDM 2007), 2007
Probabilistic latent semantic indexing (PLSI) represents documents of a collection as mixture proportions of latent topics, which are learned from the collection by an expectation maximization (EM) algorithm. New documents or queries need to be folded into the latent topic space by a simplified version of the EM-algorithm.
Alexander Hinneburg, Hans-Henning Gabriel, Andrè Gohr   +2 more
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