Abstract. In this paper we consider the time dependent one-dimensional Schrödinger equation with multiple Dirac delta potentials of different positive strengths. We prove that the classical dispersion property holds. The result is obtained in a more general setting of a Laplace operator on a tree with δ-coupling conditions at the vertices. The proof relies on a careful analysis of the propertie...

Starting from the classic definitions of resolvent set and spectrum of a linear bounded operator on a Banach space, we introduce the local resolvent set and local spectrum, the local spectral space and the single-valued extension property of a family of linear bounded operators on a Banach space. Keeping the analogy with the classic case, we extend some of the known results from the case of a l...

We propound a systematic and formal method to compute the Galois group of a non-necessarily irreducible polynomial: we proceed by successive inclusions, using mostly computations on scalars (and very few on polynomials). It is based on a formal method of specialization of relative resolvents: it consists in expressing the generic coeecients of the resolvent using the powers of a primitive eleme...

In this paper, a new monotonicity, M(·, ·)-monotonicity,is introduced in Banach spaces, and the resolvent operator of an M(·, ·)monotone operator is proved to be single valued and Lipschitz continuous. By using the resolvent operator technique associated with M(·, ·)monotone operators, we construct a proximal point algorithm for solving a class of variational inclusions. And we prove the conver...

The main purpose of this paper is to investigate almost periodic properties of various classes of (a, k)-regularized C-resolvent families in Banach spaces. We contemplate the work of many other authors working in this field, giving also some original contributions and applications. In general case, (a, k)regularized C-resolvent families under our considerations are degenerate and their subgener...

In this paper we consider Dirac operators in R, n ≥ 2, with a potential V . Under mild decay and continuity assumptions on V and some spectral assumptions on the operator, we prove a limiting absorption principle for the resolvent, which implies a family of Strichartz estimates for the linear Dirac equation. For large potentials the dynamical estimates are not an immediate corollary of the free...

For a large class of operators H a formula for the resolvent will be derived and suucient conditions will be given in order that the resolvent difference (H?z) ?1 ?(H 0 ?z) ?1 is compact resp. the wave operators (H; H 0) exist and are complete; here H 0 denotes the free quantum mechanical Hamil-tonian. The mentioned class of operators contains, a.o., the generator of a Brownian motion with kill...

The paper is devoted to an invertible linear operator whose inverse is a Hilbert Schmidt operator and imaginary Hermitian component is bounded. Numerous regular differential and integro-differential operators satisfy these conditions. A sharp norm estimate for the resolvent of the considered operator is established. It gives us estimates for the semigroup and so-called Hirsch operator functions...

We will develop the machinery of resultants and resolvent polynomials with the ultimate goal of understanding the so-called “resolvent method” for computing Galois groups over Q. Along the way, we will encounter tangential applications of these tools, such as the determination of the minimal polynomial of, say, the sum of two algebraic numbers using resultants. In this way, this paper can serve...

We give a new characterization of the solvability of an abstract Cauchy problems in terms of moment sequences, using the resolvent operator at only one point.