On the complexity of the approximate table representation of discrete analogs of functions of finite smoothness in the metric ofL P

1998 ◽  
Vol 64 (5) ◽  
pp. 557-561
Author(s):  
G. G. Amanzhaev
Keyword(s):  
Discrete Analogs ◽  
Finite Smoothness

Discrete analogs of inequalities of Wirtinger

1955 ◽  
Vol 59 (2) ◽  
pp. 73-90 ◽  
Author(s):  
Ky Fan ◽  
Olga Taussky ◽  
John Todd
Keyword(s):  
Discrete Analogs

scholarly journals Algebraic methods in discrete analogs of the Kakeya problem

2010 ◽  
Vol 225 (5) ◽  
pp. 2828-2839 ◽  
Author(s):  
Larry Guth ◽  
Nets Hawk Katz
Keyword(s):  
Algebraic Methods ◽  
Kakeya Problem ◽  
Discrete Analogs

scholarly journals Well-Posedness of the Cauchy Problem for Hyperbolic Equations with Non-Lipschitz Coefficients

2009 ◽  
Vol 2009 ◽  
pp. 1-15
Author(s):  
Akbar B. Aliev ◽  
Gulnara D. Shukurova
Keyword(s):  
Cauchy Problem ◽  
Hyperbolic Equations ◽  
Well Posedness ◽  
Singular Coefficients ◽  
The Cauchy Problem ◽  
Finite Smoothness

We consider hyperbolic equations with anisotropic elliptic part and some non-Lipschitz coefficients. We prove well-posedness of the corresponding Cauchy problem in some functional spaces. These functional spaces have finite smoothness with respect to variables corresponding to regular coefficients and infinite smoothness with respect to variables corresponding to singular coefficients.

Convergence and applications of reproducing kernels for classes of discrete harmonic functions

1974 ◽  
Vol 11 (3) ◽  
pp. 339-358
Author(s):  
C. Wayne Mastin
Keyword(s):  
Harmonic Functions ◽  
Reproducing Kernels ◽  
Biharmonic Operator ◽  
Convergence Properties ◽  
Interpolation Problems ◽  
Discrete Analogs ◽  
Discrete Harmonic Functions

This paper gives convergence properties and applications of the discrete analogs of reproducing kernels for various families of harmonic functions. From these results information is obtained on the solution of interpolation problems, the convergence of the discrete Neumann's function, and the solution to problems involving the discrete biharmonic operator.

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