Results from the now-classical distribution theory involving convolution and Fourier transformation are extended to cater for Colombeau's generalized functions. Indications are given how these particular generalized functions can be used to investigate linear equations and pseudo differential operators. Furthermore, applications are also given to problems with nonregular data.
Results from the now-classical distribution theory involving convolution and Fourier transformation are extended to cater for Colombeau's generalized functions. Indications are given how these particular generalized functions can be used to investigate linear equations and pseudo differential operators. Furthermore, applications are also given to problems with nonregular data.
Over the past few years a certain shift of focus within the theory of algebras of generalized functions (in the sense of J. F. Colombeau) has taken place. Originating in infinite dimensional analysis and initially applied mainly to problems in nonlinear partial differential equations involving singularities, the theory has undergone a change both in in ternal structure and scope of applicability, due to a growing number of applications to questions of a more geometric nature. The present book is intended to provide an in-depth presentation of these develop ments comprising its structural aspects within the theory of generalized functions as well as a (selective but, as we hope, representative) set of applications. This main purpose of the book is accompanied by a number of sub ordinate goals which we were aiming at when arranging the material included here. First, despite the fact that by now several excellent mono graphs on Colombeau algebras are available, we have decided to give a self-contained introduction to the field in Chapter 1. Our motivation for this decision derives from two main features of our approach. On the one hand, in contrast to other treatments of the subject we base our intro duction to the field on the so-called special variant of the algebras, which makes many of the fundamental ideas of the field particularly transpar ent and at the same time facilitates and motivates the introduction of the more involved concepts treated later in the chapter.
A masterful and thorough revision of the only single-source, authoritative reference on cutaneous lymphoproliferative disease. Classic reference for unsurpassed coverage of lymphocytic infiltrates of the human skin Covers a broad spectrum of topics ranging from the role of the immune system in the pathogenesis of cutaneous lymphocytic infiltrates to one describing the immunohistochemica nd molecular aspects of lymphoid neoplasia. Each chapter contains an extensive array of ‘clinical vignettes’ clearly showing the application of principles and treatment techniques discussed in the chapter Presents a succinct and logical approach to the diagnosis of most cutaneous lymphocytic infiltrates and discusses the interplay between the immune system in the propagation of lymphocytic infiltrates focusing on the role of iatrogenic and endogenous immune dysregulation. The molecular and cytogenetic basis of lymphoid neoplasia is considered in great detail. Contains hundreds of full-color, high-quality clinical and histologic photographs, with over 200 new images in the new edition
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