Related papers: A jump operator on the Weihrauch degrees
We improve known estimates for the number of points of bounded height in semigroup orbits of polarized dynamical systems. In particular, we give exact asymptotics for generic semigroups acting on the projective line. The main new ingredient…
For the time development of a single system in the quantum jump approach or for quantum trajectories one requires the conditional (reduced) Hamiltonian between jumps and the reset operator after a jump. Explicit expressions for them are…
Some preliminaries and basic facts regarding unbounded Wiener-Hopf operators (WH) are provided. WH with rational symbols are studied in detail showing that they are densely defined closed and have finite dimensional kernels and deficiency…
It is shown how to define difference operators and equations on particular lattices $\{x_n\}$, $2n\in\mathbb{Z}$, such that the divided difference operator $(\mathcal{D}f)(x_{n+1/2})= (f(x_{n+1})-f(x_n))/(x_{n+1}-x_n)$ has the property that…
We define co-Toeplitz operators, a new class of Hilbert space operators, in order to define a co-Toeplitz quantization scheme that is dual to the Toeplitz quantization scheme introduced by the author in the setting of symbols that come from…
Let $L$ be the operator defined on $C^2$ functions by $$L f(x)=\int[f(x+h)-f(x)-1_{(|h|\leq 1)}\nabla f(x)\cdot h]\frac{n(x,h)}{|h|^{d+\alpha(x)}}dh.$$ This is an operator of variable order and the corresponding process is of pure jump…
Weihrauch reducibility is a notion of reducibility between computational problems that is useful to calibrate the uniform computational strength of a multivalued function. It complements the analysis of mathematical theorems done in reverse…
In one dimension, the exponential position operators introduced in a theory of polarization are identified with the twisting operators appearing in the Lieb-Schultz-Mattis argument, and their finite-size expectation values $z_L$ measure the…
We introduce the notion of joint torsion for several commuting operators satisfying a Fredholm condition. This new secondary invariant takes values in the group of invertibles of a field. It is constructed by comparing determinants…
The author has introduced in a recent paper a new class of operators, called co-Toeplitz operators, with symbols in a co-algebra. This is the categorical dual to Toeplitz operators which have symbols in an algebra. The mapping from a symbol…
We give a necessary condition and a sufficient condition on the Banach lattices E and F so that an operator from E to F is DW-compact whenever its adjoint is DW-compact. We do the same, with different conditions, for DW-DP operators.…
The purpose of this survey is a comprehensive study of operator Lip\-schitz functions. A continuous function $f$ on the real line ${\Bbb R}$ os called operator Lipschitz if $\|f(A)-f(B)\|\le\operatorname{const}\|A-B\|$ for arbitrary…
A quasi-Hermitian operator is an operator that is similar to its adjoint in some sense, via a metric operator, i.e., a strictly positive self-adjoint operator. Whereas those metric operators are in general assumed to be bounded, we analyze…
A periodic one-dimensional Schroedinger operator is called semifinite-gap if every second gap in its spectrum is eventually closed. We construct explicit examples of semifinite-gap Schroedinger operators in trigonometric functions by…
Martin's Conjecture states that every definable function on the Turing degrees is either constant or increasing, and that every increasing function is an iterate of the Turing jump. This classification has already been corroborated for the…
Differential operators usually result in derivatives expressed as a ratio of differentials. For all but the simplest derivatives, these ratios are typically not algebraically manipulable, but must be held together as a unit in order to…
This paper is the first in a series of papers developing a functional-analytic theory of vertex (operator) algebras and their representations. For an arbitrary Z-graded finitely-generated vertex algebra (V, Y, 1) satisfying the standard…
The present paper deals with complemented lattices where, however, a unary operation of complementation is not explicitly assumed. This means that an element can have several complements. The mapping $^+$ assigning to each element $a$ the…
The notion of a Levi operator is an operator abstraction of the Levy property of a norm or, more generally of the Levi topology on a locally solid vector lattice. Various aspects of Levi operators have been studied recently by several…
We present a concrete and explicit construction of a new scalar constraint operator for loop quantum gravity. The operator is defined on the recently introduced space of partially diffeomorphism invariant states, and this space is preserved…