A construction of multiresolution analysis by integral equations
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- by Dong-Myung Lee, Jung-Gon Lee and Sun-Ho Yoon
- Proc. Amer. Math. Soc. 130 (2002), 3555-3563
- DOI: https://doi.org/10.1090/S0002-9939-02-06713-8
- Published electronically: July 2, 2002
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Abstract:
In this paper we present a versatile construction of multiresolution analysis of two variables by means of eigenvalue problems of the integral equation, for $\lambda =2$. As a consequence we show that if $\phi (x)$ is the solution of the equation $\phi (x) = \lambda \int _{\mathbb {R}} h (2x-y) \phi (y)dy$ with $supp \hat h(\omega ) = [-\pi , \pi ]$, then $V_{j} =span \{ \phi (2^{j} x_{1} -k_{1} )$ $\phi (2^{j} x_{2} -k_{2} ) | k_{1} , k_{2} \in \mathbb {Z} \}$ constructs a two-variable multiresolution analysis.References
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Bibliographic Information
- Dong-Myung Lee
- Affiliation: College of Mathematics Science, Won Kwang University, 344-2 Shinyongdong Ik-San, Chunbuk 570-749, Korea
- Email: dmlee@wonkwang.ac.kr
- Jung-Gon Lee
- Affiliation: College of Mathematics Science, Won Kwang University, 344-2 Shinyongdong Ik-San, Chunbuk 570-749, Korea
- Sun-Ho Yoon
- Affiliation: College of Mathematics Science, Won Kwang University, 344-2 Shinyongdong Ik-San, Chunbuk 570-749, Korea
- Received by editor(s): August 23, 2000
- Published electronically: July 2, 2002
- Additional Notes: This paper was supported by Won Kwang University in 2002
- Communicated by: Christopher D. Sogge
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 3555-3563
- MSC (2000): Primary 41A17, 42C15, 46A45, 46C99
- DOI: https://doi.org/10.1090/S0002-9939-02-06713-8
- MathSciNet review: 1920033