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The Weighted Hermite Polynomials Form a Basis for L2(ℝ)

William Johnston
The American Mathematical Monthly
Vol. 121, No. 3 (March 2014), pp. 249-253
DOI: 10.4169/amer.math.monthly.121.03.249
Stable URL: http://www.jstor.org/stable/10.4169/amer.math.monthly.121.03.249
Page Count: 5
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The Weighted Hermite Polynomials Form a Basis for L2(ℝ)
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Abstract

Abstract We present a student-friendly proof that the weighted Hermite polynomials form a complete orthonormal system (a basis) for the collection L2(ℝ) of real-valued functions.

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