Jacobi Condition for Elliptic Forms in Hilbert Spaces

$G$-Frames for operators in Hilbert spaces

$K$-frames as a generalization of frames were introduced by L. Gu{a}vruc{t}a to study atomic systems on Hilbert spaces which allows, in a stable way, to reconstruct elements from the range of the bounded linear operator $K$ in a Hilbert space. Recently some generalizations of this concept are introduced and some of its difference with ordinary frames are studied. In this paper, we give a new ge...

Memorandum on Dimension Formulas for Spaces of Jacobi Forms

We state ready to compute dimension formulas for the spaces of Jacobi cusp forms of integral weight k and integral scalar index m on subgroups of SL(2,Z).

Minimization of Constrained Quadratic Forms in Hilbert Spaces

A common optimization problem is the minimization of a symmetric positive definite quadratic form 〈x, Tx〉 under linear constraints. The solution to this problem may be given using the Moore–Penrose inverse matrix. In this work at first we extend this result to infinite dimensional complex Hilbert spaces, where a generalization is given for positive operators not necessarily invertible, consider...

Elliptic curves, Hilbert modular forms, and the Hodge conjecture

1.2. The first result of this type is due to Eichler ([E]) who treated the case where f = f11 is the unique weight 2 newform for Γ0(11) and E is the compactified modular curve for this group. Later, in several works, Shimura showed that the Hasse-Weil zeta functions of special models (often called canonical models) of modular and quaternionic curves are, at almost all finite places v, products ...

Generalized Frames in Hilbert Spaces