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In this paper we define the Lp-mixed curvature function of a convex body. We develop a formula connection the support function of Lp-mixed projection body with Fourier transform of the Lp-mixed curvature function. Using this formula we solve an analog of the Shephard projection problem for Lp-mixed projection bodies.
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참고문헌 (17)
참고문헌 신청
A. Koldobsky / 1998 / Intersection bodies, positive definite distributions, and the Busemann-Petty problem / Amer. J. Math. 120 (4) : 827 ~ 840
A. Koldobsky / 1999 / A generalization of the Busemann-Petty problem on sections of convex bodies / Israel J. Math. 110 : 75 ~ 91
A. Koldobsky / 2004 / Projections of convex bodies and the Fourier transform / Israel J. Math. 139 : 361 ~ 380
A. Koldobsky / 2005 / Fourier Analysis in Convex Geometry / American Mathematical Society
A. Zvavitch / 2005 / The Busemann-Petty problem for arbitrary measures / Math. Ann. 331 (4) : 867 ~ 887
A. Koldobsky / 1999 / A generalization of the Busemann-Petty problem on sections of convex bodies / Israel J. Math. 110 : 75 ~ 91
A. Koldobsky / 2004 / Projections of convex bodies and the Fourier transform / Israel J. Math. 139 : 361 ~ 380
A. Koldobsky / 2005 / Fourier Analysis in Convex Geometry / American Mathematical Society
A. Zvavitch / 2005 / The Busemann-Petty problem for arbitrary measures / Math. Ann. 331 (4) : 867 ~ 887
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