Operator (computer programming)

About: Operator (computer programming) is a research topic. Over the lifetime, 40896 publications have been published within this topic receiving 671452 citations. The topic is also known as: operator symbol & operator name.

Symmetries of Schrödinger operator with point interactions

Abstract: The transformations of all the Schrodinger operators with point interactions in dimension one under space reflection P, time reversal T and (Weyl) scaling Wλ are presented. In particular, those operators which are invariant (possibly up to a scale) are selected. Some recent papers on related topics are commented upon.

Scale-Space: Its Natural Operators and Differential Invariants

Abstract: Why and how one should study a scale-space is prescribed by the universal physical law of scale invariance, expressed by the so-called Pi-theorem. The fact that any image is a physical observable with an inner and outer scale bound, necessarily gives rise to a ‘scale-space representation’, in which a given image is represented by a one-dimensional family of images representing that image on various levels of inner spatial scale. An early vision system is completely ignorant of the geometry of its input. Its primary task is to establish this geometry at any available scale. The absence of geometrical knowledge poses additional constraints on the construction of a scale-space, notably linearity, spatial shift invariance and isotropy, thereby defining a complete hierarchical family of scaled partial differential operators: the Gaussian kernel (the lowest order, rescaling operator) and its linear partial derivatives. They enable local image analysis in a robust way, while at the same time capturing global features through the extra scale degree of freedom. The operations of scaling and differentiation cannot be separated. This framework permits us to construct in a systematic way multiscale, orthogonal differential invariants, i.e. true image descriptors that exhibit manifest invariance with respect to a change of cartesian coordinates. The scale-space operators closely resemble the receptive field profiles in the mammalian front-end visual system.

The dependence of the generalized Radon transform on defining measures

Abstract: ABsmAcr. Guillemin proved that the generalized Radon transform R and its dual R' are Fourier integral operators and that R'R is an elliptic pseudodifferential operator. In this paper we investigate the dependence of the Radon transform on the defining measures. In the general case we calculate the symbol of R'R as a pseudodifferential operator in terms of the measures and give a necessary condition on the defining measures for R'R to be invertible by a differential operator. Then we examine the Radon transform on points and hyperplanes in RX with general measures and we calculate the symbol of R'R in terms of the defining measures. Finally, if R'R is a translation invariant operator on RI then we prove that R'R is invertible and that our condition is equivalent to (R'R)' being a differential operator.