# REPRESENTATION OF INTEGRAL OPERATORS ON W22(Ω) OF REPRODUCING KERNELS

• LEE, DONG-MYUNG (Department of Mathematics Won Kwang University) ;
• LEE, JEONG-GON (Department of Mathematics Won Kwang University) ;
• CUI, MING-GEN (Harbin Institute of Technology (WEI HAI branch Institute))
• Published : 2004.12.25
• 42 3

#### Abstract

We prove that if ${\mathbb{K}}^*$ is adjoint operator on $W_2{^2}({\Omega})$, then ${\mathbb{K}}^*v(t,\;{\tau})=,\;v(x,\;y){\in}W_2{^2}({\Omega})$ ; it is also related to the decomposition of solution of Fredholm equations.

#### Keywords

Absolutely continuous;Fredholm equation;Integral operator;Reproducing Kernel

#### References

1. Trans. Amer. Math. Soc. v.68 Theory of reproducing kernels Aronszajn, N.
2. Gabor frames for $L^2$ and related spaces, in wavelets : Mathematics and Applications Benedetto, J.;Walnut, D.;Benedetto, J.(ed.);Frazier, M.(ed.)
3. Numer. Math. J. Chinese univ. v.11 no.1 Analytic solutions for Fredholm integral equation of the second kind Cui, M.
4. Math. Numerica Sinica v.8 no.2 On the best operator of interpolation in W$W^1_2$ (a, b)
5. Proc. Amer. Math. Soc. v.130 A Construction of Multiresolution Analysis by Integral equations Lee, D.M.;Lee, J.G.;Yoon, S.H.
6. J. Korea Soc. Math. Ed. Ser. B: Pure Appl. Math. v.11 no.2 Representation of solutions of Fredholm equations in $W^2_2({\Omega})$ of reproducing kernels Lee, D.M.;Lee, J.G.;Cui, M.G.
7. Integral transforms, reproducing kernels and their applications Saitoh, S.
8. Fourier Transforms and Wavelet Analysis Cui, M.G.;Lee, D.M.;Lee, J.G.
9. Theory of reproducing kernels and its applications