Zobrazeno 1 - 10
of 668
pro vyhledávání: '"34M35"'
Autor:
Nikolaev, Nikita
We prove that formal WKB solutions of Schr\"odinger equations on Riemann surfaces are resurgent. Specifically, they are Borel summable in almost all directions and their Borel transforms admit endless analytic continuation away from a discrete subset
Externí odkaz:
http://arxiv.org/abs/2410.17224
Autor:
Cotti, Giordano, Varchenko, Alexander
We consider the joint system of equivariant quantum differential equations (qDE) and qKZ difference equations for the Grassmannian $G(k,n)$, which parametrizes $k$-dimensional subspaces of $\mathbb{C}^n$. First, we establish a connection between this
Externí odkaz:
http://arxiv.org/abs/2409.09657
We provide a full classification scheme for exceptional Jacobi operators and polynomials. The classification contains six degeneracy classes according to whether $\alpha,\beta$ or $\alpha\pm\beta$ assume integer values. Exceptional Jacobi operators a
Externí odkaz:
http://arxiv.org/abs/2409.02656
We study the harmonic locus consisting of the monodromy-free Schr\"odinger operators with rational potential and quadratic growth at infinity. It is known after Oblomkov that it can be identified with the set of all partitions via the Wronskian map f
Externí odkaz:
http://arxiv.org/abs/2404.18471
Below we study a linear differential equation $\MM (v(z,\eta))=\eta^M{v(z,\eta)}$, where $\eta>0$ is a large spectral parameter and $\MM=\sum_{k=1}^{M}\rho_{k}(z)\frac{d^k}{dz^k},\; M\ge 2$ is a differential operator with polynomial coefficients such
Externí odkaz:
http://arxiv.org/abs/2402.19087
Autor:
Dell'Atti, Marta, Kecker, Thomas
Some new Hamiltonian systems of quasi-Painlev\'e type are presented and their Okamoto's space of initial conditions computed. Using the geometric approach that was introduced originally for the identification problem of Painlev\'e equations, comparin
Externí odkaz:
http://arxiv.org/abs/2402.19053
Autor:
Oshima, Toshio
As a generalization of Riemann-Liouville integral, we introduce integral transformations of convergent power series which can be applied to hypergeometric functions with several variables.
Comment: 25pages
Comment: 25pages
Externí odkaz:
http://arxiv.org/abs/2311.08947
We solve the problem of determining under which conditions the monodromy of a vanishing cycle generates the whole homology of a regular fiber for a polynomial $f(x,y)=g(x)+h(y)$ where $h$ and $g$ are polynomials with real coefficients having real cri
Externí odkaz:
http://arxiv.org/abs/2311.05563
In this paper, we consider systems of linear ordinary differential equations, with analytic coefficients on big sectorial domains, which are asymptotically diagonal for large values of $|z|$. Inspired by N. Levinson's work [Lev48], we introduce two c
Externí odkaz:
http://arxiv.org/abs/2310.19739
Complexity of Puiseux solutions of differential and $q$-difference equations of order and degree one
We relate the complexity of both differential and $q$-difference equations of order one and degree one and their solutions. Our point of view is to show that if the solutions are complicated, the initial equation is complicated too. In this spirit, w
Externí odkaz:
http://arxiv.org/abs/2310.15409