Related papers: Riesz bases from orthonormal bases by replacement

We give a complete description of Riesz bases of reproducing kernels in small Fock spaces. This characterization is in the spirit of the well known Kadets--Ingham 1/4 theorem for Paley--Wiener spaces. Contrarily to the situation in…

In this paper we obtain necessary and sufficient conditions for a linear bounded operator in a Hilbert space $H$ to have a three-diagonal complex symmetric matrix with non-zero elements on the first sub-diagonal in an orthonormal basis in…

We deal with the as yet unresolved exponential stability problem for Beck's Problem on a metric star graph with three identical edges. The edges are stretched Euler--Bernoulli beams which are simply supported with respect to the outer…

Mutually unbiased bases of a Hilbert space can be constructed by partitioning a unitary error basis. We consider this construction when the unitary error basis is a nice error basis. We show that the number of resulting mutually unbiased…

In this paper, our focus lies on a fundamental geometric invariant known as Riesz capacity, which holds an essential position in potential theory. We establish the Hadamard variational formula for Riesz capacity of convex bodies. As a…

We study a special class of (real or complex) robust Hadamard matrices, distinguished by the property that their projection onto a $2$-dimensional subspace forms a Hadamard matrix. It is shown that such a matrix of order $n$ exists, if…

We consider existence and uniqueness of symmetric approximation of frames by normalized tight frames and of symmetric orthogonalization of bases by orthonormal bases in Hilbert spaces H . More precisely, we determine whether a given frame…

It is known that self-adjoint Hamiltonians with purely discrete eigenvalues can be written as (infinite) linear combination of mutually orthogonal projectors with eigenvalues as coefficients of the expansion. The projectors are defined by…

Let $a$, $b$ be two fixed non-zero constants. A measurable set $E\subset \mathbb{R}$ is called a Weyl-Heisenberg frame set for $(a, b)$ if the function $g=\chi_{E}$ generates a Weyl-Heisenberg frame for $L^2(\mathbb{R})$ under modulates by…

In a Dedekind complete Riesz space, $E$, we show that if $(P_n)$ is a sequence of band projections in $E$ then $$\limsup\limits_{n\to \infty} P_n - \liminf\limits_{n\to \infty} P_n = \limsup\limits_{n\to \infty} P_n(I-P_{n+1}).$$ This…

Recently [Karimipour and Memarzadeh, PhysRevA 73, 012329 (2006)] posed the problem of finding a continuous family of orthonormal bases in a bipartite space of two identical systems with the following properties: i) in each basis, all states…

For extra-large Coxeter systems (m(s,r)>3), we construct a natural and explicit set of Soergel bimodules D={D_w}_{w\in W} such that each D_w contains as a direct summand (or is equal to) the indecomposable Soergel bimodule B_w. When…

Mutually unbiased bases in Hilbert spaces of finite dimensions are closely related to the quantal notion of complementarity. An alternative proof of existence of a maximal collection of N+1 mutually unbiased bases in Hilbert spaces of prime…

We extend to several dimensions the result of K. Seip and Y.I. Lyubarskii that proves the existence of Riesz basis of exponentials for a finite union of intervals with equals lengths.

The most fundamental notion in frame theory is the frame expansion of a vector. Although it is well known that these expansions are unconditionally convergent series, no characterizations of the unconditional constant were known. This has…

We present a Riesz integral representation theory in which functions, operators and measures take values in uniform commutative monoids (a commutative monoid with a uniformity making the binary operation of the monoid uniformly continuous).…

We show that any finite dimensional von Neumann algebra admits an orthonormal unitary basis with respect to its standard trace. We also show that a finite dimensional von Neumann subalgebra of $M_n(\mathbb{C})$ admits an orthonormal unitary…

We use integration by parts formulas to give estimates for the $L^p$ norm of the Riesz transform. This is motivated by the representation formula for conditional expectations of functionals on the Wiener space already given in Malliavin and…

In a scale of Fock spaces $\mathcal F_\varphi$ with radial weights $\varphi$ we study the existence of Riesz bases of (normalized) reproducing kernels. We prove that these spaces possess such bases if and only if $\varphi(x)$ grows at most…

For $2\le p<\infty$ we show the lower estimates \[ \|A^{\frac 12}x\|_p \kl c(p)\max\{\pl \|\Gamma(x,x)^{{1/2}}\|_p,\pl \|\Gamma(x^*,x^*)^{{1/2}}\|_p\} \] for the Riesz transform associated to a semigroup $(T_t)$ of completely positive maps…