Semi-Orthogonal Parseval Wavelets Frames on Local Fields and Applications in Manufacturing Science

Manufacturing science focuses on understanding problems from the perspective of the stakeholders involved and then applying manufacturing science as needed. We investigate semi-orthogonal frame wavelets and Parseval frame wavelets in L-2 (R) with a dilation factor. We show that every affine subspace is the orthogonal direct sum of at most three purely non-reducing subspaces. This result is obtained through considering the basicquestion as to when the orthogonal complement of an afffine subspace in another one is still affine subspace.The definition of multiple pseudofames for subspaces with integer translation is proposed. The notion of a generalized multiresolution structure of L-2 (R) is also introduced. The construction of a generalized multiresolution structure of Paley-Wiener subspaces of L-2 (R) is investigated.