In this article the spectral theorem for right linear compact normal operators on quaternionic Hilbert spaces is proved. Though the version of spectral theorem for such operators in quaternionic Hilbert space is appeared in recent literature using the left multiplication and considering the Hilbert space to be slice complex linear, we present a different approach, which is similar to the classi...

where x(z) = ∑∞ j=1 xjz j is the symbol of the operator. In terms of the Hardy polarization of odd spinors on S, B1(x) = P+MxP−, where P+, P− are projections and Mx is the multiplication operator corresponding to x. The map x 7−→ B1(x) is conformally equivariant in a sense explained in §2. In this paper we derive explicit expressions for certain well-known higher-order generalizations of this m...

We study the index theory of a class perturbed Dirac operators on non-compact manifolds form D+ic(X), where c(X) is Clifford multiplication operator by an orbital vector field with respect to action compact Lie group. Our main result that such factors as KK-product certain KK-theory classes defined D and X. As corollary we obtain excision cobordism-invariance properties first established Braver...

We present the Operator Language (OL), a framework to automatically generate fast numerical kernels. OL provides the structure to extend the program generation system Spiral beyond the transform domain. Using OL, we show how to automatically generate library functionality for the fast Fourier transform and multiple non-transform kernels, including matrix-matrix multiplication, synthetic apertur...

with ∆z being a small extrapolation step. The advantage of computation in the kx, ky-ω domain is that the desired result is obtained by multiplication of the data with the operator. However, to allow laterally varying medium functions a space variant convolution operator in the x, y-ω (space-frequency) domain should be applied. When the spatial extrapolation operator is used in an explicit recu...

The spectral bound, s(αA + βV), of a combination of a resolvent positive linear operator A and an operator of multiplication V, was shown by Kato to be convex in β ∈ R. Kato's result is shown here to imply, through an elementary "dual convexity" lemma, that s(αA + βV) is also convex in α > 0, and notably, ∂s(αA + βV)/∂α ≤ s(A). Diffusions typically have s(A) ≤ 0, so that for diffusions with spa...

We propose two new multilinear operators for expressing the matrix compositions that are needed in the Tucker and PARAFAC (CANDECOMP) decompositions. The first operator, which we call the Tucker operator, is shorthand for performing an n-mode matrix multiplication for every mode of a given tensor and can be employed to consisely express the Tucker decomposition. The second operator, which we ca...

A complete mesh generation or mesh adaptation process usually requires a large number of operators : Delaunay insertion, edge-face-element point insertion, edge collapse, point smoothing, face/edge swaps, etc. Independently of the complexity of the geometry, the more operators are involved in a remeshing process, the less robust the process may become. In addition, deriving a parallel version o...

We show that two unitary representations of R of very different spectral type can give rise to the same one-parameter group of "-automorphisms of a C*-algebra. Arveson [1] has introduced a spectral theory for automorphism groups on C*-algebras. However, little seems to be known about the spectral type of such groups. The fact that two unitary representations of R of very different spectral prop...

Let La be a Bergman space. We are interested in an intermediate Hankel operator H M φ from La to a closed subspace M of L 2 which is invariant under the multiplication by the coordinate function z. It is well known that there do not exist any nonzero finite rank big Hankel operators, but we are studying same types in case H φ is close to big Hankel operator. As a result, we give a necessary and...