相关论文: A remark on the matrix Airy function
By using Cauchy integral formula in the theory of complex functions, the authors establish some integral representations for the principal branches of several complex functions involving the logarithmic function, find some properties, such…
In a generalized Airy matrix model, a power $p$ replaces the cubic term of the Airy model introduced by Kontsevich. The parameter $p$ corresponds to Witten's spin index in the theory of intersection numbers of moduli space of curves. A…
In this paper, we investigate the Euler-type integral representations for the generalized hypergeometric matrix function and develop some transformations in terms of hypergeometric matrix functions. Furthermore, unit and half arguments have…
We describe a method to evaluate integrals that arise in the asymptotic analysis when two saddle points may be close together. These integrals, which appear in problems from optics, acoustics or quantum mechanics as well as in a wide class…
We consider certain scalar product of symmetric functions which is parameterized by a function $r$ and an integer $n$. One the one hand we have a fermionic representation of this scalar product. On the other hand we get a representation of…
We derive a new representation for the Weyl function associated with the complex Jacobi matrix in the finite and semi-infinite cases. In our approach we exploit connections to the discrete-time dynamical system associated with these…
An integral representation is provided for the parabolic cylinder function product $D_{\mu}(x)D_{\mu}(-y)$ where $Re\,\mu<0$ and $x>y$ are unrelated. A few simple consequences are given in the form of hyperbolic integrals and a sum rule.
There were some errors in paper hep-th/9303018 in formulas 6.1, 6.6, 6.8, 6.11. These errors have been corrected in the present version of this paper. There are also some minor changes in the introduction.
In this paper, we study the bicomplex version of the Paley-Weiner theorem and the Cauchy integral formula in the upper half-plane.
This paper derives new integral representations for products of two parabolic cylinder functions. In particular, expressions are obtained for D_{nu}(x)D_{mu}(y), with x>0 and y>0, that allow for different orders and arguments in the two…
Estimates of some integrals related to variations of smooth functions are presented.
In this paper polynomial maps are represented by the use of matrices whose entries are numbered by pair of multiindices and a new product of such matrices is introduced. A matrix representation of composition of polynomial maps is given. In…
An integral representation result for strictly positive subharmonic functions of a one-dimensional regular diffusion is established. More precisely, any such function can be written as a linear combination of an increasing and a decreasing…
New sufficient conditions for representation of a function of several variables as an absolutely convergent Fourier integral are obtained in the paper.
Gabcke proved a new integral expression for the auxiliary Riemann function \[\mathop{\mathcal R}(s)=2^{s/2}\pi^{s/2}e^{\pi i(s-1)/4}\int_{-\frac12\searrow\frac12} \frac{e^{-\pi i u^2/2+\pi i u}}{2i\cos\pi u}U(s-\tfrac12,\sqrt{2\pi}e^{\pi…
A new integral representation for the Riemann zeta function is derived. This representation covers the important region of the complex plane where the real part of the argument of the function lies between 0 and 1. Using this…
A conjecture concerning some pairs of interfering estimates for some integrals is formulated in three equivalent versions. Its importance for the the Paley problem for plurisubharmonic functions and for certain classes of extremal problems…
We propose a totally functional view of geometric matrix completion problem. Differently from existing work, we propose a novel regularization inspired from the functional map literature that is more interpretable and theoretically sound.…
Another approach to constructing an upper bound for the Riemann-Farey sum is described.
A characterization of multiplicative (and additive) arithmetical functions is given. Using this characterization, we show that the group of multiplicative arithmetical functions is isomorphic to the group of additive arithmetical functions.