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147 results on '"Balogh, F."'

5. Isotropic Grassmannians, Plücker and Cartan maps.

Author

Balogh, F., Harnad, J., and Hurtubise, J.

Subjects
*GRASSMANN manifolds, *VECTOR spaces, *IDENTITY (Psychology), *NATURAL products
Abstract

This work is motivated by the relation between the KP and BKP integrable hierarchies, whose τ-functions may be viewed as flows of sections of dual determinantal and Pfaffian line bundles over infinite dimensional Grassmannians. In finite dimensions, we show how to relate the Cartan map, which, for a vector space V of dimension N, embeds the Grassmannian G r V 0 (V + V * ) of maximal isotropic subspaces of V + V*, with respect to the natural scalar product, into the projectivization of the exterior space Λ(V), and the Plücker map, which embeds the Grassmannian GrV(V + V*) of all N-planes in V + V* into the projectivization of ΛN(V + V*). The Plücker coordinates on G r V 0 (V + V * ) are expressed bilinearly in terms of the Cartan coordinates, which are holomorphic sections of the dual Pfaffian line bundle P f * → G r V 0 (V + V * , Q). In terms of affine coordinates on the big cell, this is equivalent to an identity of Cauchy–Binet type, expressing the determinants of square submatrices of a skew symmetric N × N matrix as bilinear sums over the Pfaffians of their principal minors. [ABSTRACT FROM AUTHOR]

Published
2021
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6. Finite Dimensional KP \tau-functions I. Finite Grassmannians

Author

Balogh, F., Fonseca, T., and Harnad, J.

Subjects
High Energy Physics - Theory, Nonlinear Sciences - Exactly Solvable and Integrable Systems, Mathematical Physics
Abstract

We study \tau-functions of the KP hierarchy in terms of abelian group actions on finite dimensional Grassmannians, viewed as subquotients of the Hilbert space Grassmannians of Sato, Segal and Wilson. A determinantal formula of Gekhtman and Kasman involving exponentials of finite dimensional matrices is shown to follow naturally from such reductions. All reduced flows of exponential type generated by matrices with arbitrary nondegenerate Jordan forms are derived, both in the Grassmannian setting and within the fermionic operator formalism. A slightly more general determinantal formula involving resolvents of the matrices generating the flow, valid on the big cell of the Grassmannian, is also derived. An explicit expression is deduced for the Pl\"ucker coordinates appearing as coefficients in the Schur function expansion of the \tau-function., Comment: 45 pages. References updated

Published
2014

7. Some Biorthogonal Families of Polynomials Arising in Noncommutative Quantum Mechanics

Author

Balogh, F., Shah, Nurisya M., and Ali, S. Twareque

Subjects
Mathematics::Classical Analysis and ODEs, FOS: Physical sciences, Mathematical Physics (math-ph), Mathematical Physics
Abstract

In this paper we study families of complex Hermite polynomials and construct deformed versions of them, using a $GL(2,\mathbb{C})$ transformation. This construction leads to the emergence of biorthogonal families of deformed complex Hermite polynomials, which we then study in the context of a two-dimensional model of noncommutative quantum mechanics., 17 pages

Published
2013

8. Book reviews

Author

Szendrői, Z., Sarlós, I., Tankó, A., Balogh, F., Pethe, Gy., and Meggyes, B.

Published
1974
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11. Book reviews

Author

Jungmayer, J., Balogh, F., Rényi-Vámos, F., Szendrői, Z., Kelemen, Zs., Frang, D., Szabó, L., and Molnár, J.

Published
1976
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14. Book reviews

Author

Szendrői, Z., Beregi, E., Balogh, F., Csellár, M., Pugachev, A., Frang, D., Pytel, A., and Pethe, Gy.

Published
1976
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18. Book reviews

Author

Rényi-Vámos, F., Szabó, L., Pethe, Gy., Endes, P., Szendrői, Z., and Balogh, F.

Published
1975
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19. Book reviews

Author

Corradi, Gy., Rényi-Vámos, F., Sendrői, Z., Frang, D., Légrády, J., and Balogh, F.

Published
1974
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20. Book reviews

Author

Kelemen, B., Sarlós, J., Kiss, D., Tamás, A., Horváth, B., Szendrői, Z., Horváth, S., Tóth, P., Balogh, F., Romics, I., Szalay, L., Király, K., and Kovács, Z.

Published
1986
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21. Book reviews

Author

Szendrői, Z., Kovács, T., Szendrői, M., Tóth, I., Szabó, K., Solymossy, E., Thán, Z., Balogh, F., Tankó, A., Szendrői, Z., Szendrői, M., Papp, G., Kiss, D., Kovács, E., Takácsy, L., and Sarlós, J.

Published
1983
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29. Book reviews

Author

Corradi, Gy., Scultéty, S., Balogh, F., Szendrői, Z., Rényi-Vámos, F., Csontai, A., and Pásztor, H.

Published
1973
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32. Book reviews

Author

Rózsa, L., Rényi-Vámos, F., Pásztor, M., Balogh, F., Eckhardt, S., Szendrői, Z., Tankó, A., and Laskina, A.

Published
1973
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33. Book review

Author

Pytel, A., Rényi-Vámos, F., Járay, J., Rosdy, E., Szendrői, Z., Balogh, F., Láncos, F., Fehér, T., and Rosdy, E.

Published
1972
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36. Book reviews

Author

Szendrői, Z., Balogh, F., Pásztor, M., Rényi-Vámos, F., Verebélyi, A., Rosdy, E., Tóth, J., Rusakov, V., Burghele, Th., and Gimes, R.

Published
1973
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37. On the norms and roots of orthogonal polynomials in the plane and $L^p$-optimal polynomials with respect to varying weights

Author

Balogh, F. and Bertola, M.

Subjects
Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, FOS: Physical sciences, Mathematical Physics (math-ph), Mathematical Physics
Abstract

For a measure on a subset of the complex plane we consider $L^p$-optimal weighted polynomials, namely, monic polynomials of degree $n$ with a varying weight of the form $w^n = {\rm e}^{-n V}$ which minimize the $L^p$-norms, $1 \leq p \leq \infty$. It is shown that eventually all but a uniformly bounded number of the roots of the $L^p$-optimal polynomials lie within a small neighborhood of the support of a certain equilibrium measure; asymptotics for the $n$th roots of the $L^p$ norms are also provided. The case $p=\infty$ is well known and corresponds to weighted Chebyshev polynomials; the case $p=2$ corresponding to orthogonal polynomials as well as any other $1\leq p

Published
2009

43. Finite dimensional Kadomtsev-Petviashvili τ-functions. I. Finite Grassmannians.

Author

Balogh, F., Fonseca, T., and Harnad, J.

Subjects
*KADOMTSEV-Petviashvili equation, *GRASSMANN manifolds, *HILBERT space, *SCHUR functions, *FREDHOLM operators
Abstract

We study τ -functions of the Kadomtsev-Petviashvili hierarchy in terms of abelian group actions on finite dimensional Grassmannians, viewed as subquotients of the Hilbert space Grassmannians of Sato, Segal, and Wilson. A determinantal formula of Gekhtman and Kasman involving exponentials of finite dimensional matrices is shown to follow naturally from such reductions. All reduced flows of exponential type generated by matrices with arbitrary nondegenerate Jordan forms are derived, both in the Grassmannian setting and within the fermionic operator formalism. A slightly more general determinantal formula involving resolvents of the matrices generating the flow, valid on the big cell of the Grassmannian, is also derived. An explicit expression is deduced for the Plücker coordinates appearing as coefficients in the Schur function expansion of the τ -function. [ABSTRACT FROM AUTHOR]

Published
2014
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44. Regularity of a vector potential problem and its spectral curve

Author

Balogh, F. and Bertola, M.

Subjects
*VECTOR fields, *ALGEBRAIC curves, *BIORTHOGONAL systems, *POLYNOMIALS, *MATHEMATICAL analysis, *FUNCTIONAL analysis
Abstract

Abstract: In this note we study a minimization problem for a vector of measures subject to a prescribed interaction matrix in the presence of external potentials. The conductors are allowed to have zero distance from each other but the external potentials satisfy a growth condition near the common points. We then specialize the setting to a specific problem on the real line which arises in the study of certain biorthogonal polynomials (studied elsewhere) and we prove that the equilibrium measures solve a pseudo-algebraic curve under the assumption that the potentials are real analytic. In particular, the supports of the equilibrium measures are shown to consist of a finite union of compact intervals. [Copyright &y& Elsevier]

Published
2009
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