On Hamburger Moments Problem Generated by a Group With Two Limit Points

© 2018, Allerton Press, Inc. We study a linear four-element equation in the class of solutions that are holomorphic outside an isosceles trapezium and vanish at infinity. The equation is used here to investigate the Hamburger moments problem for entire functions of exponential type

ON THE DIFFERENCE EQUATION ASSOCIATED WITH THE DOUBLY PERIODIC GROUP AND ITS APPLICATIONS

Let D be a rectangle. We consider a four-element linear difference equation defined on D. The shifts of this equation are the generating transformations of the corresponding doubly periodic group and their inverse transformations. We search for a solution in the class of functions that are holomorphic outside D and vanish at infinity. Their boundary values satisfy a H¨older condition on any compact that does not contain the vertices. At the vertices, we allow, at most, logarithmic singularities. The independent term is holomorphic on D, and its boundary value satisfies a H¨older condition. The independent term may not be analytically continuable across an interval of the boundary, since the solution and the independent term belong to different classes of analytical functions. We regularize the difference equation and determine the conditions for the regularization to be equivalent. If the independent term is an odd function, then the problem is solvable. Additionally, we give some applications of the difference operator to interpolation problems for integer functions of exponential type and the construction of biorthogonally conjugated systems of analytical function

Manifestation of New Interference Effects in Superconductor/Ferromagnet Spin Valve

Superconductor/ferromagnet (S/F) spin valve effect theories based on the S/F proximity phenomenon assume that the superconducting transition temperature Tc of F1/F2/S or F1/S/F2 trilayers for parallel magnetizations of the F1- and F2-layers (TcP) are smaller than for the antiparallel orientations (TcAP). Here, we report for CoOx/Fe1/Cu/Fe2/In multilayered systems with varying Fe2-layer thickness the sign-changing oscillating behavior of the spin valve effect \Delta Tc=TcAP-TcP. Our measurements revealed the full direct spin valve effect with TcAP>TcP for Fe2-layer thickness dFe2<1 nm and the full inverse (TcAP=1 nm. Interference of Cooper pair wave functions reflected from both surfaces of the Fe2-layer appear as the most probable reason for the observed behavior of \Delta Tc.Comment: Accepted for publication in PR

Evidence for Triplet Superconductivity in a Superconductor-Ferromagnet Spin Valve

We have studied the dependence of the superconducting (SC) transition temperature on the mutual orientation of magnetizations of Fe1 and Fe2 layers in the spin valve system CoO_x/Fe1/Cu/Fe2/Pb. We find that this dependence is nonmonotonic when passing from the parallel to the antiparallel case and reveals a distinct minimum near the orthogonal configuration. The analysis of the data in the framework of the SC triplet spin valve theory gives direct evidence for the long-range triplet superconductivity arising due to noncollinearity of the two magnetizations.Comment: 5 pages (including 4 EPS figures). Version 2: final version as published in PR

Experimental Observation of the Inverse Proximity Effect in Superconductor/Ferromagnet Layered Structures

We have studied the nuclear magnetic resonance (NMR) of 51V nuclei in the superconductor/ferromagnet thin film heterostructures Ni/V/Ni and Pd{1-x}Fe{x}/V/Pd{1-x}Fe{x} in the normaland superconducting state. Whereas the position and shape of the NMR line in the normal state for the trilayers is identical to that observed in a single V-layer, in the superconducting state the line shape definitely changes, developing a systematic distortion of the high-field wing of the resonance line. We consider this as the first experimental evidence for the penetration of ferromagnetism into the superconducting layer, a phenomenon which has been theoretically predicted recently and dubbed the inverse proximity effect.Comment: about 5 pages, 3 figures, 1 tabl

On Hamburger Moments Problem Generated by a Group With Two Limit Points

© 2018, Allerton Press, Inc. We study a linear four-element equation in the class of solutions that are holomorphic outside an isosceles trapezium and vanish at infinity. The equation is used here to investigate the Hamburger moments problem for entire functions of exponential type