Lane-Emden systemNonexistenceWe establish necessary conditions for the convergence of multiple Fourier series of integrable functions in the mean.doi:10.1007/s11253-011-0566-0P. V. ZadereiO. V. IvashchukSpringer USUkrainian Mathematical Journal...
Journal of Approximation TheoryA. Mate, P. Nevai, and V. Totik, Necessary conditions for weighted mean convergence of Fourier series in orthogonal polynomials, J. Approx. Theory 46 (1986), 314 322.A. Máté, P. Nevai and V. Totik, Necessary conditions for mean convergence of Fourier ...
Let T = [−π,π) be the one dimensional torus and suppose X to be one of the spaces C(TN) or LP(TN), 1≦p< ∞. The k-th modulus of smoothness of a function f in X is defined by...
We extend the results of A.S. Belov from single to double Fourier series, which give necessary conditions in terms of the Fourier coefficients for L1-convergence. Our basic tools are Hardy's inequality for the Taylor coefficients of a function in the Hardy space H1 on the unit disk, and ...
Proving the convergence of the integrals for these choices of φ and ψ proceeds much as in our previous example. Since the details are similar, we focus on the function K, which has a different structure than in the previous case. To proceed, we suppose that ...
Necessary and sufficient conditions for the basis property in L p , and equiconvergence with a trigonometric series, of spectral decompositions and expansi... Let G be a bounded interval of the real line and let L denote the differential expression Lu=u (n) +p 1 u (n-1) +···+p ...
Dirichlet Series Dirichlet test for convergence Dirichlet theorem Dirichlet transform Dirichlet, Peter Gustav Lejeune Dirichlet's conditions dirigible Dirk Dirk Jan Struik Dirk Volkertszoon Coornhert Dirksen, Everett Dirksen, Everett McKinley Dirr, Adolf ...
Publisher's description: Originally published in 1986, this valuable reference provides a detailed treatment of limit theorems and inequalities for empiric... GR Shorack,JA Wellner - 《Series in Statistics》 被引量: 434发表: 1987年 POINTWISE CONVERGENCE OF FOURIER SERIES Let f be a piecewise cont...
Periodic boundary correction refers to the process of mapping coordinates from the trajectory to equivalent coordinates, subject to the periodic boundary conditions (PBCs), such that the trajectory is physically consistent over time: for example, atoms in a protein which exit the periodic box on one...
system of functional equations is proved. The method of successive approximations is used in combination with the method of contraction mapping. The unique solution of the impulsive mixed problem is obtained in the form of Fourier series. Absolutely and uniformly convergence of Fourier series is ...