Frames and bases for mathematics and engineering: an introductory course

Based on a streamlined presentation of the author’s successful work An Introduction to Frames and Riesz Bases, this new textbook develops frame theory as part of a dialogue between mathematicians and engineers. Newly added sections on applications will help mathematically oriented readers to see where frames are used in practice and engineers to discover the mathematical background for applications in their field. The primary focus of the work is on basic topics without too many side remarks making it easier for students to follow the presentation. An introductory chapter presents basic results in finite-dimensionalvector spaces, enabling readers with a basic knowledge of linear algebra to understand the idea behind frames without the technical complications in infinite-dimensional spaces. Extensive exercises make the work suitable as a textbook for use in theoretical graduate courses on bases and frames or applications-oriented courses focusing on either Gabor analysis or wavelets. Interdisciplinary approach develops frame theory as part of a dialogue between mathematicians, and engineers INDICE: Preface.- Frames in Finite-dimensional Inner Product Spaces.- Infinite-dimensional Vector Spaces and Sequences.- Bases.- Bases and their Limitations.- Frames in Hilbert Spaces.- Frames of Translates.- Gabor Frames in L2(R).- Selected Topics on Gabor Frames.- Gabor Frames in l2(Z).- Wavelet Frames.- Wavelet Frames via Extension Principles.- Appendix.- References.- Index.

• ISBN: 978-0-8176-4677-6
• Editorial: BIRKHAUSER VERLAG.
• Encuadernacion: Rústica
• Páginas: 242
• Fecha Publicación: 01/01/2008
• Nº Volúmenes: 1
• Idioma: Inglés