Spectrum of Convolution Dilation Operators on Weighted L P Spaces

  title={Spectrum of Convolution Dilation Operators on Weighted L P Spaces},
  author={Xiaojie Gao and S. L. Lee and Qiyu Sun},
R c(x)dx = 1. For any sufficiently large number K the space Lp([−K,K]) of all Lp-functions with support in the interval [−K,K] is an invariant space of Wc,α. It is known that Wc,α restricted to Lp([−K,K]) is a compact operator with eigenvalues α−k, k = 0, 1, . . . , and spectrum {α−k : k = 1, 2, . . .} ∪ {0}, which are independent of c and K. This result is better understood in the context of weighted Lp space, Lw(R) that comprises functions f for which fw belong to Lp(R). We prove that under… CONTINUE READING

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