Frames for Undergraduates

Deguang Han: University of Central Florida, Orlando, FL,Keri Kornelson: Grinnell College, Grinnell, IA,David Larson: Texas A&M University, College Station, TX,Eric Weber: Iowa State University, Ames, IA

出版者:American Mathematical Society

作者:Deguang Han

页数:295

出版时间:2007

价格:0

isbn号码:9780821842126

丛书系列:Student Mathematical Library

图书标签:科普Spy

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A frame in a finite-dimensional inner-product space is a collection of vectors spanning this space. In this sense, frames are generalizations of orthonormal bases, which can be used in many cases where orthonormal bases cannot be tailored to fit naturally arising applications. The wide array of possibilities introduced by working with frames rather than orthonormal bases has revolutionized mathematical areas such as wavelets and harmonic analysis. The adaptability to existing conditions allows frames to be used in applied settings including signal processing, imaging, sampling, and cryptography.

The study of frames, particularly in finite dimensions, begins with exactly the topics from an undergraduate linear algebra course. This makes the topics particularly accessible to undergraduate students, yet the theory contains deep unsolved problems. This book can be used as a resource for an REU or for a topics course about frames. It is also a suitable textbook for a second linear algebra course, using frames as a thematic example to demonstrate and explore the new material.

The theory of frames is increasingly broad with widespread applications. "Frames for Undergraduates" introduces students to this vibrant and important area of mathematics.