The transformed values ẑpk are complex, but for each value of p the ẑ p k form a Hermitian sequence (i.e., ẑpn k is the complex conjugate of ẑ p k), so they are completely determined by mn real numbers (since ẑ p 0 is real, as is ẑpn=2 for n even). Alternatively, given m Hermitian sequences of n complex data values zpj , this routine simultaneously calculates their inverse (backward) discrete F...

In this paper we consider holomorphically projective mappings from equiaffine spaces onto almost Hermitian spaces. We found the equations of these mappings in the form of a system of linear Cauchy equations. These results generalize the results obtained for holomorphically projective mappings of Kählerian spaces by J. Mikeš and analogous results about K-spaces and Hspaces obtained by I.N. Kurba...

It is shown that a large part of the cohomology of the classifying space of a Lie group satisfying certain hypotheses can be obtained by a difference construction from hermitian representations of that Lie group. This result is relevant to the study of Novikov’s higher signatures. 1. Statement of the Theorem 1.1. Let G be a connected Lie group. We set H G = H(BG,C) (cohomology with complex coef...

For a given standard Hamiltonian H = [p − A(x)]2/(2m) + V (x) with arbitrary complex scalar potential V and vector potential A, with x ∈ R, we construct an invertible antilinear operator τ such that H is τ -anti-pseudo-Hermitian, i.e., H = τHτ−1. We use this result to give the explicit form of a linear Hermitian invertible operator with respect to which any standard PT -symmetric Hamiltonian wi...

— A statement in the paper “Holomorphic Morse inequalities on manifolds with boundary” saying that the holomorphic Morse inequalities for an hermitian line bundle L over X are sharp as long as L extends as semi-positive bundle over a Stein-filling is corrected, by adding certain assumptions. A more general situation is also treated. Résumé. — Nous corrigeons l’énoncé qui affirme que les inégali...

We classify all linear operators $A:V\to V$ satisfying $(Au,v)=(u,A^rv)$ and $(Au,A^rv)=(u,v)$ with $r=2,3,\dots$ on a complex, real, or quaternion vector space scalar product given by nonsingular symmetric, skew-symmetric, Hermitian, skew-Hermitian form.

Let k be a field of characteristic different from 2. Let E/k be a finite separable extension with a k-linear involution σ. For every σ-symmetric element μ ∈ E∗, we define a hermitian scaled trace form by x ∈ E 7→ TrE/k(μxx). If μ = 1, it is called a hermitian trace form. In the following, we show that every even-dimensional quadratic form over a hilbertian field, which is not isomorphic to the ...

Consider the sequence of poles A = {α1, α2, . . .}, and suppose the rational functions φn with poles inA form an orthonormal system with respect to an Hermitian positive-definite inner product. Further, assume the φn satisfy a three-term recurrence relation. Let the rational function φ n\1 with poles in {α2, α3, . . .} represent the associated rational function of φn of order 1; i.e. the φ n\1 ...

Consider the sequence of polesA = {α1, α2, . . .}, and suppose the rational functions φj with poles in A form an orthonormal system with respect to a Hermitian positive-definite inner product. Further, assume the φj satisfy a three-term recurrence relation. Let the rational function φ j\1 with poles in {α2, α3, . . .} represent the associated rational function of φj of order 1; i.e. the φ (1) j...