arXiv subjects
Publications and source records attributed to 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 procedure, the generalization is easy. This, however, helps to obtain general information regarding FQ operations, and to generalize the symmetric orthogonalization procedure.
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.
The $H$-ring structure of certain infinite(-dimensional) Grassmannians is discussed using various algebraic and analytical methods but so that cellular arguments are avoided. These methods allow us to discuss these Grassmannian in greater generality.
We examine the validity of certain spectral integral formulas in topological rings. We consider the sign and square-root functions in polymetric rings containing $\frac12$. It turns out that formal analogues of classical transformation kernels and the resolvent identity can be used to understand the situation. In the lack of $\frac12$, the functions $\frac12-\frac12\sgn(\frac12-z)$ and $\frac12-\sqrt{\frac14-z}$ can be generalized, respectively.
Analytical tools to $K$-theory; namely, self-stabilization of rapidly decreasing matrices, linearization of cyclic loops, and the contractibility of the pointed stable Toeplitz algebra are discussed in terms of concrete formulas. Adaptation to the *-algebra and finite perturbation categories is also considered. Moreover, the finite linearizability of algebraically finite cyclic loops is demonstrated.
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 algebraic nature of this factorization.
We give an alternative proof for the Mathai-Quillen formula for a Thom form using its natural behaviour with respect to fiberwise integration. We also study this phenomenon in general context.
We discuss linearization of skew-periodic loops. We generalize the situation to linearization of non-commutative loops and $\mathbb S^1$-cocycles.