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Colloquium, Spring 2005

Day: Thursday May 19th Time: 4:00pm Place: BH 227 Title: The Fourier Transform, and no applications Speaker: Mark DeSmet, WWU The Fourier Transform is a well known transform which appears in fields ranging from applied physics to oceanography. It describes a function in terms of its frequencies. Within mathematics the Fourier Transform has applications to diverse areas, from partial differential equations to algebraic number theory. In my talk, I will address none of theses exciting applications. I will instead first introduce the Fourier Transform and discuss some of its basic properties. I will then present an intuitive "proof with pictures" of one the most important results relating to the Fourier Transform, the Plancherel Theorem. This theorem extends the definition of the transform to a Hilbert space on which it is invertible. Attendees should leave with a basic understanding of how and where the Fourier Transform is defined and have a grasp on the proof of the Plancherel Theorem. Cookies: In BH 300 at 3:30pm.