2 citations · 10 across the 26 of their papers we have counts for
27 papers
The elliptical range theorem for the conformal range
Gyula Lakos
The conformal range (or the real Davis--Wielandt shell), which is a particular planar projection of the Davis--Wielandt shell, can be considered as the hyperbolic version of the nu…
Hyperbolic elliptic parabolic disks approximated by half distance bands
Gyula Lakos
Hyperbolic elliptic parabolic disks can be described by the inequality () in the unit disk based Beltrami--Cayley--Klein model of the hyperbol…
Convergence estimates for the Magnus expansion IE. Finite dimensional Banach algebras
Gyula Lakos
We review and provide simplified proofs related to the Magnus expansion, and improve convergence estimates. Observations and improvements concerning the Baker--Campbell--Hausdorff…
On averaged self-distances in finite dimensional Banach spaces
Gyula Lakos
Assume that is a real Banach space of finite dimension . Consider any Borel probability measure supported on the unit ball of . We show t…
The noncommutative heat equation and certain Lie series
Gyula Lakos
We approach the convergence of the Magnus, Wilcox, and symmetric Wilcox expansions by a non-commutative heat equation derived from the Maurer-Cartan equation.
The Dynkin-Specht-Wever lemma and some associated constructions
Gyula Lakos
In the first part of the paper, some extensions of the classical Dynkin-Specht-Wever lemma are developed. In the second part, we extend Burgunder's splitting construction, and rela…
The symmetric Poincaré-Birkhoff-Witt theorem and Dynkin-Magnus commutators
Gyula Lakos
The objective of this paper is to give alternative proofs for the symmetric Poincaré-Birkhoff-Witt theorem utilizing the Magnus recursion formulae or Dynkin's non-commutative polyn…
Alternating patterns in commutator monomials
Gyula Lakos
Considering commutator monomials of the non-commutative associative variables ; we determine the maximal possible number of alternating associative monomials in the…
Convergence estimates for the Magnus expansion IA. Uniformly convex algebras
Gyula Lakos
We review and provide simplified proofs related to the Magnus expansion, and improve convergence estimates. Observations and improvements concerning the Baker--Campbell--Hausdorff…
Convergence estimates for the Magnus expansion IIA. matrices with operator norm
Gyula Lakos
We review and provide simplified proofs related to the Magnus expansion, and improve convergence estimates. Observations and improvements concerning the Baker--Campbell--Hausdorff…
On the elliptical range theorems for the Davis-Wielandt shell, the numerical range, and the conformal range
Gyula Lakos
We consider the elliptical range theorems for the Davis--Wielandt shell, the numerical range, and the conformal range in terms of and related to their quadratic representations. Th…
A short proof of the elliptical range theorem
Gyula Lakos
A short proof of the elliptical range theorem concerning the numerical range of complex matrices is given.
Convergence estimates for the Magnus expansion III. Banach--Lie algebras
Gyula Lakos
We review and provide simplified proofs related to the Magnus expansion, and improve convergence estimates. Observations and improvements concerning the Baker--Campbell--Hausdorff…
Convergence estimates for the Magnus expansion II. -algebras
Gyula Lakos
We review and provide simplified proofs related to the Magnus expansion, and improve convergence estimates. Observations and improvements concerning the Baker--Campbell--Hausdorff…
Some proofs of the Poincaré-Birkhoff-Witt theorem and related matters
Gyula Lakos
This expository paper focuses on free Lie -algebras and the basic PBW theorem. We argue in various ways that the basic PBW theorem is a quite close consequence of the Magnus-Wit…
Convergence estimates for the Magnus expansion I. Banach algebras
Gyula Lakos
We review and provide simplified proofs related to the Magnus expansion, and improve convergence estimates. Observations and improvements concerning the Baker--Campbell--Hausdorff…
Fermionic quantum operations: a computational framework II. Examples, monoaxiality, scalings
Gyula Lakos
The objective of this series of papers is to recover information regarding the behaviour of FQ operations in the case , and FQ conform-operations in the case . In this se…
Fermionic quantum operations: a computational framework I. Basic invariance properties
Gyula Lakos
The objective of this series of papers is to recover information regarding the behaviour of FQ operations in the case , and FQ conform-operations in the case . In this fi…
Fermionic quantum orthogonalizations I
Gyula Lakos
We generalize classical orthogonalization procedures from real linear algebra to the setting of fermionic quantum (FQ) operations. In the case of the Gram-Schmidt orthogonalization…
On the -ring structure of infinite Grassmannians
Gyula Lakos
The -ring structure of certain infinite(-dimensional) Grassmannians is discussed using various algebraic and analytical methods but so that cellular arguments are avoided. These…
Linearization of skew-periodic loops and -cocycles
Gyula Lakos
We discuss linearization of skew-periodic loops. We generalize the situation to linearization of non-commutative loops and -cocycles.
Factorization of Laurent series over commutative rings
Gyula Lakos
We generalize the Wiener-Hopf factorization of Laurent series to more general commutative coefficient rings, and we give explicit formulas for the decomposition. We emphasize the a…
Spectral calculations on locally convex vector spaces I
Gyula Lakos
We develop a holomorphic functional calculus for (multivalued linear) operators on locally convex vector spaces. This includes the case of fractional powers along Lipschitz curves.
Spectral calculations in rings
Gyula Lakos
We examine the validity of certain spectral integral formulas in topological rings. We consider the sign and square-root functions in polymetric rings containing . It turn…