Department of Mathematics
Recent Submissions

Elementary proofs of some identities of Ramanujan for the RogersRamanujan functions
(Elsevier, 20120401)In a handwritten manuscript published with his lost notebook, Ramanujan stated without proofs forty identities for the RogersRamanujan functions. With one exception all of Ramanujan's identities were proved. In this paper, ... 
On lifting of operators to Hilbert spaces induced by positive selfadjoint operators
(Elsevier, 20050415)We introduce the notion of induced Hilbert spaces for positive unbounded operators and show that the energy spaces associated to several classical boundary value problems for partial differential operators are relevant ... 
A theorem of Jon F. Carlson on filtrations of modules
(Elsevier, 200701)We give an alternative proof to a theorem of Carlson [J.F. Carlson, Cohomology and induction from elementary abelian subgroups, Quart. J. Math. 51 (2000) 169181] which states that if G is a finite group and k is a field ... 
A filtration of the modularrepresentation functor
(Elsevier, 20071201)Let F and K be algebraically closed fields of characteristics p > 0 and 0, respectively. For any finite group G we denote by K RF (G) = K ⊗Z G0 (F G) the modular representation algebra of G over K where G0 (F G) is the ... 
Free actions on products of spheres at high dimensions
(Mathematical Sciences Publishers, 20130531)A classical conjecture in transformation group theory states that if G = (Z/p)(r) acts freely on a product of k spheres Sn1 x ... x Snk, then r <= k. We prove this conjecture in the case where the dimensions {n(i)} are ... 
A generalization of a modular identity of Rogers
(Elsevier, 200906)In a handwritten manuscript published with his lost notebook, Ramanujan stated without proofs forty identities for the RogersRamanujan functions. Most of the elementary proofs given for these identities are based on ... 
Uniqueness of Gibbs states in onedimensional antiferromagnetic model with longrange interaction
(American Institute of Physics, 199910)Uniqueness of Gibbs states in the onedimensional antiferromagnetic model with very longrange interaction is established. © 1999 American Institute of Physics. 
Genotypes of irreducible representations of finite pgroups
(Elsevier, 20061215)For any characteristic zero coefficient field, an irreducible representation of a finite pgroup can be assigned a Roquette pgroup, called the genotype. This has already been done by Bouc and Kronstein in the special cases ... 
Triplets of Closely Embedded Dirichlet type spaces on the Unit Polydisc
(Springer Basel, 2013)We propose a general concept of triplet of Hilbert spaces with closed embeddings, instead of continuous ones, and we show how rather general weighted L2 spaces yield this kind of generalized triplets of Hilbert spaces for ... 
On a problem of H.Shapiro
(Elsevier, 200402)Let μ be a real measure on the line such that its Poisson integral M(z) converges and satisfies M(x+ iy) ≤ Aecyα, y → + ∞, for some constants A, c > 0 and 0 < α ≤ 1. We show that for 1/2 < α ≤ 1 the measure μ must have ... 
On the LevyRaikovMarcinkiewicz Theorem
(Elsevier, 20030201)Let μ be a finite nonnegative Borel measure. The classical LévyRaikovMarcinkiewicz theorem states that if its Fourier transform μ̂ can be analytically continued to some complex halfneighborhood of the origin containing ... 
Set covering and Serre's theorem on the cohomology algebra of a pgroup
(Elsevier, 2001111)We define a group theoretical invariant, denoted by s(G), as a solution of a certain set covering problem and show that it is closely related to chl(G), the cohomology length of a pgroup G. By studying s(G) we improve the ... 
Family of scaling chirp functions, diffraction and holography
(Institute of Electrical and Electronics Engineers, 199507)It is observed that diffraction is a convolution operation with a chirp kernel whose argument is scaled. Family of functions obtained from a prototype by shifting and argument scaling form the essential ground for wavelet ... 
Mackey functions, induction from restriction functors and coinduction from transfer functors
(Elsevier, 20070901)Boltje's plus constructions extend two wellknown constructions on Mackey functors, the fixedpoint functor and the fixedquotient functor. In this paper, we show that the plus constructions are induction and coinduction ... 
A local version of the PawluckiPlesniak extension operator
(Elsevier, 200501)Using local interpolation of Whitney functions, we generalize the Pawłucki and Pleśniak approach to construct a continuous linear extension operator. We show the continuity of the modified operator in the case of generalized ... 
Backlund transformations for discrete Painleve equations: Discrete PIIPV
(Elsevier, 2006)Transformation properties of discrete Painleve´ equations are investigated by using an algorithmic method. This method yields explicit transformations which relates the solutions of discrete Painleve´ equations, discrete ... 
Essential cohomology for elementary abelian pgroups
(Elsevier, 200912)For an odd prime p the cohomology ring of an elementary abelian pgroup is polynomial tensor exterior. We show that the ideal of essential classes is the Steenrod closure of the class generating the top exterior power. As ... 
On the classification of Darboux integrable chains
(American Institute of Physics, 2008)We study differentialdifference equation (d/dx) t (n+1,x) =f (t (n,x),t (n+1,x), (d/dx) t (n,x)) with unknown t (n,x) depending on continuous and discrete variables x and n. Equation of such kind is called Darboux integrable, ... 
Recursion operators of some equations of hydrodynamic type
(American Institute of Physics, 200103)We give a general method for constructing recursion operators for some equations of hydrodynamic type, admitting a nonstandard Lax representation. We give several examples for N = 2 and N = 3 containing the equations of ... 
On plane sextics with double singular points
(, 2013)We compute the fundamental groups of five maximizing sextics with double singular points only; in four cases, the groups are as expected. The approach used would apply to other sextics as well, given their equations.