Let $$\mathcal {H}$$ be a complex Hilbert space with inner product $$\langle \cdot , \rangle $$ and let A non-zero bounded positive linear operator on {H}.$$ $$\mathbb {B}_A(\mathcal {H})$$ denote the algebra of all operators which admit A-adjoint, $$N_A(\cdot )$$ seminorm . The generalized A-numerical radius $$T\in \mathbb is defined as $$\begin{aligned} \omega _{N_A}(T)=\displaystyle {\sup _{...

The classical shadows protocol, recently introduced by Huang, Kueng, and Preskill [Nat. Phys. 16, 1050 (2020)], is a quantum-classical protocol to estimate properties of an unknown quantum state. Unlike full state tomography, the can be implemented on near-term hardware requires few measurements make many predictions with high success probability. In this paper, we study effects noise protocol....

In [3] Berg, Christensen and Ressel prove that the closure of the cone of sums of squares ∑R[X]2 in the polynomial ring R[X] := R[X1, . . . , Xn] in the topology induced by the `1-norm is equal to Pos([−1, 1]n), the cone consisting of all polynomials which are non-negative on the hypercube [−1, 1]n. The result is deduced as a corollary of a general result, also established in [3], which is vali...

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We study Dirichlet boundary control of Stokes flows in 2D polygonal domains. consider cost functionals with two different regularization terms: the $L^2$ norm and an energy space seminorm. prove well-posedness regularity results for both problems, develop finite element discretizations error estimates latter problem. The motivation to problem follows from our analysis: we that choice ${\bm L}^2...

We consider infinite-horizon γ-discounted Markov Decision Processes, for which it is known that there exists a stationary optimal policy. We consider the algorithm Value Iteration and the sequence of policies π1, . . . , πk it implicitely generates until some iteration k. We provide performance bounds for non-stationary policies involving the last m generated policies that reduce the state-of-t...

We develop two generalizations of contraction theory, namely, semi-contraction and weak-contraction theory. First, using the notion seminorm, we propose a geometric framework for introduce matrix semimeasures characterize their properties. show that spectral abscissa is infimum over weighted semimeasures. For dynamical systems, use semimeasure Jacobian to contractivity properties trajectories. ...

We develop the theory of Fraïssé limits for classes finite-dimensional multi-seminormed spaces, which are defined to be vector spaces equipped with a finite sequence seminorms. define notion Fréchet space and we use correspondence in this setting obtain many examples such spaces. This allows us give Fraïssé-theoretic construction (Gω,(‖⋅‖n)n<ω), separable almost universal disposition class all ...

Abstract We study a PDE-constrained optimal control problem that involves functions of bounded variation as controls and includes the TV seminorm in objective. apply path-following inexact Newton method to problems arise from smoothing adding an $$H^1$$ H 1 regularizati...

We provide necessary and sufficient conditions for a 1-jet (f,G):E→R×X to admit an extension (F,∇F) some F∈C1,ω(X). Here E stands arbitrary subset of Hilbert space X ω is modulus continuity. As corollary, in the particular case X=Rn, we obtain (nonlinear) operator whose norm does not depend on dimension n. Furthermore, construct extensions such way that: (1) (f,G)↦(F,∇F) bounded with respect na...