Titchmarsh Theorem

If is Square Integrable over the Real axis, then any one ofthe following implies the other two:

1. The Fourier Transform of is 0 for .

2. Replacing by , the function is analytic in the Complex Plane for andapproaches almost everywhere as . Furthermore, for some number and (i.e., the integral is bounded).

3. The Real and Imaginary Parts of are HilbertTransforms of each other.

• Parabiaugmented Dodecahedron
• Parabiaugmented Hexagonal Prism
• Parabiaugmented Truncated Dodecahedron
• Parabidiminished Rhombicosidodecahedron
• Parabigyrate Rhombicosidodecahedron
• Parabola
• Parabola Caustic
• Parabola Evolute
• Parabola Inverse Curve
• Parabola Involute
• Parabola Pedal Curve
• Parabolic Coordinates
• Parabolic Cyclide
• Parabolic Cylinder
• Parabolic Cylinder Function
• Parabolic Cylindrical Coordinates
• Parabolic Fixed Point
• Parabolic Geometry
• Parabolic Horn Cyclide
• Parabolic Partial Differential Equation
• Parabolic Point
• Parabolic Ring Cyclide
• Parabolic Rotation
• Parabolic Segment
• Parabolic Spindle Cyclide