Exponential bases in L2

It is proved that every space L2 (I1, ∪ I2), where I1 and I2 are finite intervals, has a Riesz basis of complex exponentials , {λk} a sequence of real numbers. A partial result for the corresponding problem for n≧3 finite intervals is also obtained.

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Interpolation of Subspaces and Applications to Exponential Bases

Nigel J. Kalton Selecta ◽

10.1007/978-3-319-18796-9_16 ◽

2015 ◽

pp. 509-532

Author(s):

Fritz Gesztesy ◽

Gilles Godefroy ◽

Loukas Grafakos ◽

Igor Verbitsky

Keyword(s):

Exponential Bases

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Frame Spectral Pairs and Exponential Bases

Journal of Fourier Analysis and Applications ◽

10.1007/s00041-021-09872-9 ◽

2021 ◽

Vol 27 (5) ◽

Author(s):

Christina Frederick ◽

Azita Mayeli

Keyword(s):

Spectral Pairs ◽

Exponential Bases

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On unconditional exponential bases in weighted spaces on interval of real axis

Lobachevskii Journal of Mathematics ◽

10.1134/s1995080217010097 ◽

2017 ◽

Vol 38 (1) ◽

pp. 48-61

Author(s):

K. P. Isaev

Keyword(s):

Real Axis ◽

Weighted Spaces ◽

Exponential Bases

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Even‐tempered atomic orbitals. II. Atomic SCF wavefunctions in terms of even‐tempered exponential bases

The Journal of Chemical Physics ◽

10.1063/1.1679962 ◽

1973 ◽

Vol 59 (11) ◽

pp. 5936-5949 ◽

Cited By ~ 202

Author(s):

Richard C. Raffenetti

Keyword(s):

Atomic Orbitals ◽

Exponential Bases

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On unconditional exponential bases in weighted spaces on real axis

Ufimskii Matematicheskii Zhurnal ◽

10.13108/2015-7-3-108 ◽

2015 ◽

Vol 7 (3) ◽

pp. 108-118

Author(s):

Artur Airatovich Yunusov

Keyword(s):

Real Axis ◽

Weighted Spaces ◽

Exponential Bases

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On exponential bases for the Sobolev spaces over an interval

Journal of Mathematical Analysis and Applications ◽

10.1016/0022-247x(82)90142-1 ◽

1982 ◽

Vol 87 (2) ◽

pp. 528-550 ◽

Cited By ~ 22

Author(s):

David L Russell

Keyword(s):

Sobolev Spaces ◽

Exponential Bases

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Concerning Exponential Bases on Multi-Rectangles of ℝ d $$\boldsymbol {\mathbb {R}^d}$$

Topics in Classical and Modern Analysis - Applied and Numerical Harmonic Analysis ◽

10.1007/978-3-030-12277-5_4 ◽

2019 ◽

pp. 65-85

Author(s):

Laura De Carli

Keyword(s):

Exponential Bases

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Exponential Bases in Sobolev Spaces in Control and Observation Problems

Optimal Control of Partial Differential Equations ◽

10.1007/978-3-0348-8691-8_3 ◽

1999 ◽

pp. 33-42

Author(s):

Sergei A. Avdonin ◽

Sergei A. Ivanov ◽

David L. Russell

Keyword(s):

Sobolev Spaces ◽

Exponential Bases

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Exponential bases in Sobolev spaces in control and observation problems for the wave equation

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500000512 ◽

2000 ◽

Vol 130 (5) ◽

pp. 947-970 ◽

Cited By ~ 7

Author(s):

S. A. Avdonin ◽

S. A. Ivanov ◽

D. L. Russell

Keyword(s):

State Space ◽

Control Systems ◽

Sobolev Spaces ◽

Fourier Method ◽

Exponential Families ◽

Control Space ◽

Space State ◽

Exponential Bases ◽

And Control ◽

Control Operators

The Fourier method in control systems reduces the study of controllability/observability to the study of related exponential families. In this paper we present examples of such systems, specifically those for which we can prove that the related exponential families form a Riesz basis in corresponding appropriately defined Sobolev spaces. This makes it possible to choose ‘natural’ pairs of spaces: the state space observability space and the control space state space, depending on whether an observation or a control problem is studied, respectively, so that the observation and control operators are isomorphisms.

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