Special Integral Operators: Weierstrass operators and related integrals |
Contents
INTEGRALS ASSOCIATED WITH THE KERNEL expax² | 1 |
THE WEIERSTRASS TRANSFORM W | 39 |
CONTENTSCONTD | 62 |
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absolutely convergent applying Fubini's theorem applying the Lebesgue Bessel functions CALIFORNIA SANTA CRUZ change of variable convergence theorem Appendix Definition derived by substituting differentiable equation exponential fe L²(R follows by applying Fourier operator Fourier transform Fourier transform multiplier fractional integral Fubini's theorem Appendix Hermite functions implies inequality Appendix 6.8 integer j>1 integer N1 integral expression integral inequality Appendix integral operators integrals indicated integrals involving inversion formula 3.2.17 ix.t dt L¹(R² L²(R² Laplacian operator Lebesgue convergence theorem Lebesgue measurable let fe LP(R measurable function Minkowski's integral inequality Monotone convergence theorem n-tuples non-increasing one-dimensional operators by parameter parameter integrals positive integer product formula proof of Theorem radial functions real numbers representation semi-group of operators theorem Appendix 6.4 variable by substituting Weierstrass kernel Weierstrass operators Weierstrass transforms Young's inequality