In this manuscript, we study the inverse problem for non self-adjoint Sturm--Liouville operator $-D^2+q$ with eigenparameter dependent boundary and discontinuity conditions inside a finite closed interval. By defining  a new Hilbert space and  using its spectral data of a kind, it is shown that the potential function can be uniquely determined by part of a set of values of eigenfunctions at som...

Chen's biharmonic conjecture is well-known and stays open: The only biharmonic submanifolds of Euclidean spaces are the minimal ones. In this paper, we consider an advanced version of the conjecture, replacing $Delta$ by its extension, $L_1$-operator ($L_1$-conjecture). The $L_1$-conjecture states that any $L_1$-biharmonic Euclidean hypersurface is 1-minimal. We prove that the $L_1$-conje...

Given a commuting d-tuple T̄ = (T1, . . . , Td) of otherwise arbitrary operators on a Hilbert space, there is an associated Dirac operator DT̄ . Significant attributes of the d-tuple are best expressed in terms of DT̄ , including the Taylor spectrum and the notion of Fredholmness. In fact, all properties of T̄ derive from its Dirac operator. We introduce a general notion of Dirac operator (in dimen...

for suitable banach spaces $x$ and $y$ with schauder decompositions and‎ ‎a suitable closed subspace $mathcal{m}$ of some compact operator space from $x$ to $y$‎, ‎it is shown that the strong banach-saks-ness of all evaluation‎ ‎operators on ${mathcal m}$ is a sufficient condition for the weak‎ ‎banach-saks property of ${mathcal m}$, where for each $xin x$ and $y^*in‎ ‎y^*$‎, ‎the evaluation op...

In this paper the Bargmann space is denoted by F. This space’s roots can be found in mathematical problem of relativistic physics or in quantum optics. In physics the Bargmann space contains the canonical coherent states, so it is the main tool for studying the bosonic coherent state theory of radiation field and for other application .This paper deals with the unilateral backward shift operato...

The author was originally led to Krĕın space operator theory by a problem of L. de Branges concerning the coefficients of univalent functions. The particular question was resolved in the negative, but the operator methods used to show this are related to other areas which remain currently active, such as the study of generalized Schur and Nevanlinna functions. The methods are of a general natur...

The idea of replacing functions by linear operators, the process of quantization, goes back to the foundations of quantum mechanics and has a great impact in mathematics. This applies for instance to representation theory, operator algebra, noncommutative geometry, quantum and free probability or operator space theory. The quantization of measure theory leads to the theory of Lp spaces defined ...