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American Institute of Mathematical Sciences. Previous Article Entire solutions with asymptotic behavior of fully nonlinear uniformly elliptic equations. Campo Grande , Lisboa, Portugal, Portugal 2. An application to the deformation quantization of one-dimensional systems with boundaries is also presented. Keywords: Quantum systems with boundaries , deformation quantization. Self-adjoint, globally defined Hamiltonian operators for systems with boundaries. References: [1] N.

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### Operators and Matrices

Wiley Google Scholar. Albeverio, S.

- Religious Ambiguity and Religious Diversity.
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London Mathematical Society Lecture Notes Cambridge University Press Google Scholar. Bennewitz, Ch. Sturm-Liouville Theory, pp. Berezanskii, Ju. American Mathematical Society, Providence, R. Buchholz, H. Springer Google Scholar. Dijksma, A. Theory Adv. Dunford, N. Sergii Torba. Albeverio a,b,c S. Email addresses: albeverio uni-bonn. Albeverio , kuzhel imath. Kuzhel , sergiy. This idea gave rise to many publications see the surveys in [18], [26]. Whatever form the p-adic models may take in the future, it has become clear that finding p-adic counterparts for all basic structures of the standard mathematical physics is an interesting task.

Kochubei [18].

- Nonlinear Processes in Engineering.
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Since there exists a p-adic analysis based on the mappings from Qp into Qp and an analysis connected with the mapping Qp into the field of complex numbers C, there exist two types of p-adic physical models. The investigation of such operators is motivated by an intensive development of pseudo-Hermitian PT -symmetric quantum mechanics in the last few years [10], [14], [22], [25], [27]. We will use the following notations: D A and ker A denote the domain and the null-space of a linear operator A, respectively. Basically we shall use the same notations as in [26]. Let p be a prime num- ber.

Denote by D Qp the linear space of locally constant functions on Qp with compact supports. This convergence determines the Schwartz topology in D Qp. On Qp there exists the Haar measure, i. Its extension by continuity onto L2 Qp determines an unitary operator in L2 Qp. The operator of differentiation is not defined in L2 Qp. Proposition 2.

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It follows from [18, Lemma 3. Theorem 2. But then, recalling 2. The comparison of 2. Assertion 1 is proved. Taking 2. Employing 2. The expression 2. Therefore, the terms of 2. Statements 1.

By Proposition 2. Lemma 2. Then: 1. The proof of Lemma 2. By virtue of Proposition 2. Taking this into account and using 2. In order to give a meaning to 3. Theorem 3. The operator AB is self-adjoint if and only if the matrix B is Hermitian. Example 1. P-self-adjoint realizations. It follows from Proposition 2. By Theorem 3.

## Ele-Math – Operators and Matrices: Volume 8

The choice of a resolvent formula has to be motivated by simple links with the parameters of the perturbations. Relations 2. It is easy to see from 2.