deficiency indices
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1: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions
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► We have a direct sum of linear spaces: .
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►So has self-adjoint extensions with deficiency indices
, or or .
…Let be the deficiency indices for restricted to , and the ones for restricted to .
…The two (equal) deficiency indices of are then equal to .
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►The above results, especially the discussions of deficiency indices and limit point and limit circle boundary conditions, lay the basis for further applications.
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2: 32.1 Special Notation
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►Unless otherwise noted, primes indicate derivatives with respect to the argument.
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3: 6.1 Special Notation
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►Unless otherwise noted, primes indicate derivatives with respect to the argument.
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4: 36.6 Scaling Relations
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Indices for -Scaling of Magnitude of or (Singularity Index)
… ►Indices for -Scaling of Coordinates
… ►Indices for -Scaling of Hypervolume
…5: Viewing DLMF Interactive 3D Graphics
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6: About MathML
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7: 12.1 Special Notation
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►Unless otherwise noted, primes indicate derivatives with respect to the variable, and fractional powers take their principal values.
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8: About Color Map
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►The four color scheme quickly indicates in which quadrant lies: the colors blue, green, red and yellow are used to indicate the first, second, third and fourth quadrants, respectively.
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9: 1.1 Special Notation
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real variables. | |
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primes | derivatives with respect to the variable, except where indicated otherwise. |
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