Inverse Sturm-Liouville problems and their applications

By Gerhard Freiling, Vjacheslav A. Yurko. 2001

766 citations recorded by the source corpus.

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Citations in the corpus

An inverse spectral problem for Sturm–Liouville operators with a large constant delay (2017, methodology): “for one and the same classical Sturm–Liouville equation with one common boundary condition uniquely determine the potential along with the coefficients of the boundary conditions (see [1,4]).”
A uniqueness theorem for the boundary value problems with non-linear dependence on the spectral parameter in the boundary conditions (2009, methodology): “Using the asymptotic estimates for the solutions of (1) [4] we derive the following estimates for ’(x, ) and (x, ).”
Spectral problems for Sturm–Liouville operator with boundary and jump conditions linearly dependent on the eigenparameter (2012, methodology): “The inverse problem for discontinuous Sturm–Liouville operator with Dirichlet conditions was given in [17] and [20].”
On half inverse problem for differential pencils with the spectral parameter in boundary conditions (2011, unknown): “, [11]) one can show that the eigenvalues ρn , n ∈ A := {n : n =±0,±1,±2, .”
Incomplete Inverse Spectral and Nodal Problems for Differential Pencils (2011, methodology): “We consider the function ϕ ( x, ρ ) for real ρ. Repeating word by word the proof of the corresponding assertion for the case q 1 ( x ) = 0 (see, e.g., Lemma 1.2.2. in [10]) one can prove that the zeros of ϕ ( x, ρ ) with respect to x are continuous functions of ρ, i.e. the following lemma holds.”
Inverse spectral problems for Sturm–Liouville operators on graphs (2005, methodology): “Thus, inverse problem 1 is a generalization of the classical inverse problems for the Sturm–Liouville operator on an interval from the Weyl function, and (which is equivalent) from the spectral measure, and from the discrete spectral data (see [ 27 ], chapter 1).”
A partial inverse problem for the Sturm–Liouville operator on a star-shaped graph (2017, methodology): “The potential qj can be uniquely recovered from its Weyl function Mj(λ) by the classical methods (see [17], [20]).”
AN INVERSE PROBLEMS FOR STURM-LIOUVILLE-TYPE DIFFERENTIAL EQUATION WITH A CONSTANT DELAY (2016, background): “More detailed of this topic can be found in the monograph [5].”
Inverse spectral problems for differential operators on arbitrary compact graphs (2010, background): “For each fixed j D 1; s and D 0; 1, these functions are the Weyl functions (see [14]) for equation (2.”
Overview to mathematical analysis for fractional diffusion equations - new mathematical aspects motivated by industrial collaboration (2010, background): “, Freiling and Yurko [9]) and the eigenfunction expansion.”
On an Inverse Spectral Problem for a Convolution Integro-differential Operator (2007, background): “The greatest success in the inverse problem theory has been achieved for the Sturm–Liouville operator (see the historical reviews in [3–5]) and afterwards for differential operators of an arbitrary order (see [1, 7, 8]).”
The Boundary Control Approach to the Titchmarsh-Weyl m–Function. I. The Response Operator and the A–Amplitude (2007, unknown): “− We emphasize that all the ingredients we use in the present paper are already known in diﬀerent inverse problems communities ([ 9 ], [ 14 ], [ 12 ], [ 6 ], [ 8 ] to name just ﬁve) but it is the new way to combine them that makes our main contribution to this well developed area.”
On inverse spectral problem for non-selfadjoint Sturm–Liouville operator on a finite interval (2007, methodology): “when q(x),h,H are real, the inverse problem of recovering L from its spectral characteristics was investigated fairly completely (see [1–7] and the references therein).”