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Chapter 1 INTEGRALS ASSOCIATED WITH THE KERNEL expallx2
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absolutely convergent applying Fubini's theorem applying Minkowski's integral applying the Lebesgue Bessel functions change of variable complex numbers contd convergence theorem Appendix Definition denoted derived by letting derived by substituting differentiating dt dy e"at eixt dt equation equivalent integral estimate evaluated follows by applying follows on letting Fourier operator Fourier transform fractional integrals Fubini's theorem Appendix Hence the result Hermite function Holder's inequality implies inequality Appendix 6.8 integral expression integral inequality Appendix integrals indicated inversion formula 3*2.17 Lebesgue convergence theorem Lebesgue measurable Lebesgue measurable function let f letting j—>oo LP(R LP(Rn measurable function Minkowski's integral inequality Monotone convergence theorem n-tuples non-increasing one-dimensional operators by parameter operators defined parameter integrals positive integer product formula proof of Theorem radial functions results involving second result semi-group of operators Suppose theorem Appendix 6.4 theorem is derived variable by substituting Weierstrass operators Young's inequality