I define canonical utility functions via an explicit formula that inherits semicontinuity, continuity, Cauchy continuity, and uniform continuity from preferences. This construction is used to (i) show Rader’s and Debreu’s theorems in a fast and transparent way, (ii) refine these results for Cauchy and uniformly continuous preferences on a metric space X , (iii) extend such preferences from X to...

This paper develops a rigorous asymptotic expansion method with its numerical scheme for the Cauchy-Dirichlet problem in second order parabolic partial differential equations (PDEs). As an application, we propose a new approximation formula for pricing a barrier option under a certain type of stochastic volatility model including the log-normal SABR model.

We prove, by simple manipulation of commutators, two noncommutative generalizations of the Cauchy–Binet formula for the determinant of a product. As special cases we obtain elementary proofs of the Capelli identity from classical invariant theory and of Turnbull’s Capelli-type identities for symmetric and antisymmetric matrices.

We prove, by simple manipulation of commutators, two noncommutative generalizations of the Cauchy–Binet formula for the determinant of a product. As special cases we obtain elementary proofs of the Capelli identity from classical invariant theory and of Turnbull’s Capelli-type identities for symmetric and antisymmetric matrices.

The paper contains a simple proof of the Finch-PatchRakesh inversion formula for the spherical mean Radon transform in odd dimensions. This transform arises in thermoacoustic tomography. Applications are given to the Cauchy problem for the Euler-Poisson-Darboux equation with initial data on the cylindrical surface. The argument relies on the idea of analytic continuation and known properties of...

We define a smooth functional calculus for a noncommuting tuple of (unbounded) operators Aj on a Banach space with real spectra and resolvents with temperate growth, by means of an iterated Cauchy formula. The construction is also extended to tuples of more general operators allowing smooth functional calculii. We also discuss the relation to the case with commuting operators.

In this paper, a new condition for the controllability of higher order linear dynamical systems is obtained. The suggested test contains rank conditions of suitably defined matrices and is based on the notion of compound matrices and the Binet-Cauchy formula.

We consider the explicit solution to axisymmetric diffusion equation. recast in form of a Mellin inversion formula, and outline method compute formula for \(u(r,t)\) as series using Cauchy residue theorem. As consequence, we are able represent equation rapidly converging series. doi:10.1017/S1446181121000110