Related papers: Thompson's theorem for II_1 factors
In this paper, we discuss the method of obtaining symmetries for second order nonhomogeneous neutral differential equations with variable coefficients. We use Taylor theorem for a function of several variables to obtain a Lie type…
We consider the analytic continuation of the transfer function associated with a 2x2 operator matrix having unbounded couplings into unphysical sheets of its Riemann surface. We construct a family of non-selfadjoint operators which…
An extension of the first eigenvalue-type Ambarzumyan's theorem are provided for the arbitrary self-adjoint Sturm-Liouville differential operators. The result makes a contribution to the P\"oschel-Trubowitz inverse spectral theory as well.
The addition relation for the Riemann theta functions and for its limits, which lead to the appearance of exponential functions in soliton type equations is discussed. The presented form of addition property resolves itself to the…
Torelli's theorem is proven by the study of the convolution product of the intersection cohomology sheaf of the thetadivisor.
Thom polynomials of singularities express the cohomology classes dual to singularity submanifolds. A stabilization property of Thom polynomials is known classically, namely that trivial unfolding does not change the Thom polynomial. In this…
We prove that for almost square tensor product grids and certain sets of bivariate polynomials the Vandermonde determinant can be factored into a product of univariate Vandermonde determinants. This result generalizes the conjecture [Lemma…
For a second-order linear differential equation with two irregular singular points of rank three, multiple Laplace-type contour integral solutions are considered. An explicit formula in terms of the Stokes multipliers is derived for the…
This paper allows one to obtain a criterion for the existence of a projectively invariant measure formulated in terms of combinatorial properties of a group (amenability of some canonical quotient group). Such necessary and sufficient…
In this paper, we first give a simple combinatorial proof of Tepper's identity. Then, as a by product of this interesting identity we present another proof of the well-known Wilson's identity in number theory. Finally, we obtain a…
For matrices with all nonnegative entries, the Perron-Frobenius theorem guarantees the existence of an eigenvector with all nonnegative components. We show that the existence of such an eigenvector is also guaranteed for a very different…
Considering a differential operator of third order that does not increase the degree of polynomials, we analyse some properties of elements of the dual space of 2-orthogonal polynomial eigenfunctions. In two classes of such generic…
The orthogonal polynomials $p_n$ satisfy Tur\'an's inequality if $p_n^2(x)-p_{n-1}(x)p_{n+1}(x)\ge 0$ for $n\ge 1$ and for all $x$ in the interval of orthogonality. We give general criteria for orthogonal polynomials to satisfy Tur\'an's…
Demushkin's Theorem says that any two toric structures on an affine variety X are conjugate in the automorphism group of X. We provide the following extension: Let an (n-1)-dimensional torus T act effectively on an n-dimensional affine…
We use earlier defined notion of $n$- determinant to investigate sub-determinants of an extended Vandermonde matrix. Firstly, we demonstrate our method on a number of particular cases. Then we prove that all these results may be stated in…
A quantitative version of the Oppenheim conjecture for inhomogeneous quadratic forms is proved. We also give an application to eigenvalue spacing on flat 2-tori with Aharonov-Bohm flux.
We give a necessary and sufficient condition for the existence of a local solution of the inverse problem of calculus of variations in terms of the identical vanishing of the variation of a functional on an extended space (with the number…
We show that Thompson's $A\times B$-Lemma can be obtained as a consequence of the Brauer pair version of Brauer's Third Main Theorem.
We present a special class of examples of automorphic lifts of multiple tensor products of automorphic representations, motivated by combinatorial identities for Schur polynomials and a celebrated result of Newton and Thorne.
A theorem of Mirsky provides necessary and sufficient conditions for the existence of an N-square complex matrix with prescribed diagonal entries and prescribed eigenvalues. We give a simple inductive proof of this theorem.