In this paper we give global characterisations of Gevrey-Roumieu and Gevrey-Beurling spaces of ultradifferentiable functions on compact Lie groups in terms of the representation theory of the group and the spectrum of the Laplace-Beltrami operator. Furthermore, we characterise their duals, the spaces of corresponding ultradistributions. For the latter, the proof is based on first obtaining the characterisation of their α-duals in the sense of Köthe and the theory of sequence spaces. We also give the corresponding characterisations on compact homogeneous spaces.
Various regularization schemes used in quantum field theory, including the widely used dimensional regularization scheme, and the concept of renormalization, are introduced through the study of scattering from an attractive Dirac delta potential in more than one dimension. This is expected to make such advanced concepts and techniques available to enthusiastic beginners within the realm of elementary quantum mechanics.
Abstract. In this paper we give a global characterisation of classes of ultradifferentiable functions and corresponding ultradistributions on a compact manifold X. The characterisation is given in terms of the eigenfunction expansion of an elliptic operator on X. This extends the result for analytic functions on compact manifolds by Seeley [See69], and the characterisation of Gevrey functions and Gevrey ultradistributions on compact Lie groups and homogeneous spaces by the authors [DR14a].
Multiple integrals with respect to fractional Brownian motion (with H > 1/2) are constructed for a large class of functions. The first and second moments of the multiple integrals are explicitly identified.Mathematics Subject Classification (1991): 60G15, 60H05
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