Product formulas for semigroups with elliptic generators |
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Authors: | Marc A Berger Alan D Sloan |
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Institution: | School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332 USA |
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Abstract: | Real constant coefficient nth order elliptic operators, Q, which generate strongly continuous semigroups on L2(k) are analyzed in terms of the elementary generator, , for n even. Integral operators are defined using the fundamental solutions pn(x, t) to ut = Au and using real polynomials ql,…, qk on m by the formula, for q = (ql,…, qk), m. It is determined when, strongly on L2(k), . If n = 2 or k = 1, this can always be done. Otherwise the symbol of Q must have a special form. |
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