Antennas with identical patterns differ to the extent in which they n~odify an incident wave, i.e., in the amount they scatter. An antenna is completely described by an (infinite dimensional) scattering matrix. The concept of a minimum scattering antenna introduced by Dicke is generalized to include antennas with a finite number of accessible waveguide ports and with non-reciprocal componants.A canoniral minimum scattering antenna is defined as on, which becomes "invisible' when the accessible waveguide term-nal.: arc. open circuited. Such an antenna is shown to be unique once the independent radiation patterns have been specified. Neither an impedance nor an --dm.ttaLce matrix for such an antenna exists.The physical significance of the' :n-iinurn scrttt-rirg antenna concept is examined from several points of view. Approirite eaecralizations of Dicke' a results are derived for mu3ktiport ari no--rezip:oczai antennas. The "scattered power 0, is introduced as a convenient measure of &c4Attering. It is demonstrated, for a large class of antennas, t•a the scaterced power is quite generally greater than the absorbed power, equality being attained for minimum scattering antennas cG this class. This result further justifies the mv 4 'niiur-scat.ering terminology.Arrays of canonical antennas are discussed briefly.
Antennas with identical patterns differ to the extent in which they n~odify an incident wave, i.e., in the amount they scatter. An antenna is completely described by an (infinite dimensional) scattering matrix. The concept of a minimum scattering antenna introduced by Dicke is generalized to include antennas with a finite number of accessible waveguide ports and with non-reciprocal componants.A canoniral minimum scattering antenna is defined as on, which becomes "invisible' when the accessible waveguide term-nal.: arc. open circuited. Such an antenna is shown to be unique once the independent radiation patterns have been specified. Neither an impedance nor an --dm.ttaLce matrix for such an antenna exists.The physical significance of the' :n-iinurn scrttt-rirg antenna concept is examined from several points of view. Approirite eaecralizations of Dicke' a results are derived for mu3ktiport ari no--rezip:oczai antennas. The "scattered power 0, is introduced as a convenient measure of &c4Attering. It is demonstrated, for a large class of antennas, t•a the scaterced power is quite generally greater than the absorbed power, equality being attained for minimum scattering antennas cG this class. This result further justifies the mv 4 'niiur-scat.ering terminology.Arrays of canonical antennas are discussed briefly.
The main point of the present paper is to derive a limit-point criterion from which the criteria of Weyl [6], Friedrichs [3] and Sears [4] follow as special cases. This limit-point criterion is an immediate consequence of a Sturm comparison theorem. It is shown to be equivalent to the criterion of Weyl [6] when use is made of a Liouville-type transformation formula. Consider the Sturm-Liouville differential operator (1) Ly =-(py')' + qy, X~ < x < X+, where, in the open interval (X~, X+), p(x) and g(x) are real and continuous and p(x) >0. Let Xo be any point where X-< Xo < X+. Definition (Weyl [6]). L is of limit-point type (abbreviated LP) at X+ if for some constant Xo not all solutions of Ly=\oy are in L2(xa, X+).
The main point of the present paper is to derive a limit-point criterion from which the criteria of Weyl [6], Friedrichs [3] and Sears [4] follow as special cases. This limit-point criterion is an immediate consequence of a Sturm comparison theorem. It is shown to be equivalent to the criterion of Weyl [6] when use is made of a Liouville-type transformation formula. Consider the Sturm-Liouville differential operator (1) Ly =-(py')' + qy, X~ < x < X+, where, in the open interval (X~, X+), p(x) and g(x) are real and continuous and p(x) >0. Let Xo be any point where X-< Xo < X+. Definition (Weyl [6]). L is of limit-point type (abbreviated LP) at X+ if for some constant Xo not all solutions of Ly=\oy are in L2(xa, X+).
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