In this paper, we compute the first two equivariant heat kernel coefficients of the Bochner Laplacian on differential forms. The first two equivariant heat kernel coefficients of the Bochner Laplacian with torsion are also given. We also study the equivariant heat kernel coefficients of nonmininmal operators on differential forms and get the equivariant Gilkey-Branson-Fulling formula. MSC: 58J0...

In this work, we introduce a theory of stochastic integration with respect to symmetric α-stable cylindrical Lévy processes. Since processes do not enjoy semi-martingale decomposition, our approach is based on decoupling inequality for the tangent sequence Radonified increments. This enables us characterise largest space predictable Hilbert-Schmidt operator-valued which are integrable an proces...

1 For multiple Fourier integrals in the place of Fourier series this formula has been previously estabLished and made use of in the paper: S. Bochner, "Ein Konvergenzsatz fur mehrvariablige Fouriersche Integrale," Math. Zeit., 34, 440-447 (1931); see also A. C. Berry, "The Fourier Transform Theorem," Jour. Math. Phys. Mass. Inst. Technology, 8, 106-118 (1929). 2 See Bochner, S., "Properties of ...

We construct wavelet Riesz bases for the usual Sobolev spaces of divergence free functions on (0, 1)n that have vanishing normals at the boundary. We give a simultaneous space-time variational formulation of the instationary Stokes equations that defines a boundedly invertible mapping between a Bochner space and the dual of another Bochner space. By equipping these Bochner spaces by tensor prod...

We discuss algebraic properties for the symbols of geometric first order differential operators on almost Hermitian manifolds and Kähler manifolds. Through study on the universal enveloping algebra and higher Casimir elements, we know algebraic relations for the symbols like the Clifford algebra. From the relations, we have all the Bochner identities for the operators. As applications, we have ...

We construct a Kähler structure (which we call a generalised Kähler cone) on an open subset of the cone of a strongly pseudo-convex CR manifold endowed with a 1-parameter family of compatible Sasaki structures. We determine those generalised Kähler cones which are Bochner-flat and we study their local geometry. We prove that any Bochner-flat Kähler manifold of complex dimension bigger than two ...

We study harmonic morphisms by placing them into the context of conformal foli-ations. Most of the results we obtain hold for bres of dimension one and codomains of dimension not equal to two. We consider foliations which produce harmonic mor-phisms on both compact and noncompact Riemannian manifolds. By using integral formulae, we prove an extension to one-dimensional foliations which produce ...