View Proposal #230
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| ID | 230 |
|---|---|
| First Name | Greg |
| Last Name | Ongie |
| Institution | Coe College |
| Speaker Category | undergraduate student |
| Title of Talk | Orthogonal Polynomials on the Cantor Set |
| Abstract | The middle-thirds Cantor set is an uncountable set of Lebesgue measure zero. The Cantor measure is defined such that it assigns the Cantor set measure one, and has the Cantor set as its support. An orthogonal polynomial sequence (OPS) is traditionally defined by means of Riemann integration, but more generally an OPS can be defined by means of integration with respect to a measure. First we construct the Cantor measure and show it satisfies the properties of a measure. Then, we verify the existence of an associated OPS by examining the positivity of its moment matrix. Finally, using the Gram-Schmidt method we construct the OPS, and derive various properties of the polynomials based on results for classical orthogonal polynomials. |
| Subject area(s) | Analysis, Measure Theory, Orthogonal Polynomials |
| Suitable for undergraduates? | Yes |
| Day Preference | |
| Computer Needed? | Y |
| Bringing a laptop? | N |
| Overhead Needed? | N |
| Software requests | |
| Special Needs | |
| Date Submitted | 3/21/2008 |
| Year | 2008 |