Wavelets and orthogonal polynomials based on harmonic oscillator eigenstates
Dao‐Qing Dai · Journal of Mathematical Physics · 2000
We present a new method for the construction of wavelets. The main tool is the harmonic oscillator eigenstates. With the help of their properties we are able to construct wavelets which have explicit expressions and have exponential decay in both time domain and frequency domain. Moreover we get a new family of polynomials which are orthogonal in a weighted squarely integrable function space.