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L p multiplier theorem for the Hodge–Kodaira operator
"... Summary. We discuss the L p multiplier theorem for a semigroup acting on vector valued functions. A typical example is the Hodge–Kodaira operator on a Riemannian manifold. We give a probabilistic proof. Our main tools are the semigroup domination and the Littlewood–Paley inequality. 1 ..."
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Summary. We discuss the L p multiplier theorem for a semigroup acting on vector valued functions. A typical example is the Hodge–Kodaira operator on a Riemannian manifold. We give a probabilistic proof. Our main tools are the semigroup domination and the Littlewood–Paley inequality. 1
Nonsymmetric diffusions on a Riemannian manifold Abstract.
"... We consider a nonsymmetric diffusion on a Riemannian manifold △ + b. We give a sufficient condition for which A generated by A = 1 2 generates a C0semigroup in L 2. To do this, we show that A is maximal dissipative. Further we give a characterization of the generator domain. We also discuss the sa ..."
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We consider a nonsymmetric diffusion on a Riemannian manifold △ + b. We give a sufficient condition for which A generated by A = 1 2 generates a C0semigroup in L 2. To do this, we show that A is maximal dissipative. Further we give a characterization of the generator domain. We also discuss the same issue in L p (1 < p < ∞) setting and give a sufficient condition for which A generates a C0semigroup in L p. We consider diffusion processes on a Riemannian manifold generated by the operator 1 △ + b. Here △ is the LaplaceBeltrami operator 2 and b is a vector field. We assume that coefficients are all C ∞. So
SCHRÖDINGER OPERATORS ON THE WIENER SPACE
"... We discuss a Schrödinger operator on the Wiener space of the form L − V, L being the OrnsteinUhlenbeck operator and V is a potential function. We determine the domain of L−V and show the spectral gap under the assumption of exponential integrability of the negative part of V. ..."
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We discuss a Schrödinger operator on the Wiener space of the form L − V, L being the OrnsteinUhlenbeck operator and V is a potential function. We determine the domain of L−V and show the spectral gap under the assumption of exponential integrability of the negative part of V.