The authors discuss the existence of pseudo almost periodic solutions of differential equations with piecewise constant argument by means of introducing new concept, pseudo almost periodic sequence.
The Shannon's sampling theorem has many extensions, two of which are to wavelet subspaces of L 2(R) and to B 2 π =:{f(x,y)∈ L 2(R 2), supp ×} , where supp denotes the support of the...The Shannon's sampling theorem has many extensions, two of which are to wavelet subspaces of L 2(R) and to B 2 π =:{f(x,y)∈ L 2(R 2), supp ×} , where supp denotes the support of the Fourier transform of a function f . In fact, the Paley Wienner theorem says that each f in B 2 π can be recovered from its sampled values {f(x n,y m)} n,m if (x n, y m) satisfies |x n-n|L<14 and |y m-m| L<14 . Unfortunately this theorem requires strongly the product structure of sampling set {(x n, y m)} m,n∈ Z . This paper gives a sampling theorem in which the sampling set has a general form {(x nm , y nm )} . In addition, G.Walter′s sampling theorem is extended to wavelet subspaces of L 2(R 2) and irregular sampling with the general sampling set {(x nm ,y nm )} is considered in the same spaces. All results in this work can be written similarly in n -dimensional case for n2 .展开更多
文摘The authors discuss the existence of pseudo almost periodic solutions of differential equations with piecewise constant argument by means of introducing new concept, pseudo almost periodic sequence.
文摘The Shannon's sampling theorem has many extensions, two of which are to wavelet subspaces of L 2(R) and to B 2 π =:{f(x,y)∈ L 2(R 2), supp ×} , where supp denotes the support of the Fourier transform of a function f . In fact, the Paley Wienner theorem says that each f in B 2 π can be recovered from its sampled values {f(x n,y m)} n,m if (x n, y m) satisfies |x n-n|L<14 and |y m-m| L<14 . Unfortunately this theorem requires strongly the product structure of sampling set {(x n, y m)} m,n∈ Z . This paper gives a sampling theorem in which the sampling set has a general form {(x nm , y nm )} . In addition, G.Walter′s sampling theorem is extended to wavelet subspaces of L 2(R 2) and irregular sampling with the general sampling set {(x nm ,y nm )} is considered in the same spaces. All results in this work can be written similarly in n -dimensional case for n2 .
