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This equality is equivalent to.

If, and are all satisfied, supposing there exists, obviously,, such that, that is, Noticing (3.3)–(3.7), this equality is equivalent to that is,.

In this paper, we present a geometric norm equality involving an admissible linear form ω for the Shilov boundary of a homogeneous Siegel domain D. We prove that the validity of this norm equality is equivalent to the symmetry of D and the reduction of ω essentially to the Koszul form.

The above equality is equivalent to.

The latter equality is equivalent to begin{array}rcl@ Pi=Pi(Sigma Pi.

The last equality is equivalent to the equality C ⋅ [ 1 − μ β − α ∑ k = 1 ∞ a k ( x ) ] = 0. We obtain from this the result that either C = 0 or ∑ k = 1 ∞ a k ( x ) = μ α − β.

A system of functions is the basis of the, and the above-mentioned equality is equivalent to the condition below (2.12).

Evidently, the above equality is equivalent to the following: T g - 1 P K r z + ρ - 1 Q K r z = 0, (5.11).

The last equality is equivalent to the couple of real equalities: 1 z 1 δ = exp - | z 2 | γ sin ( γ arg z 2 ) | z 2 | γ δ, z 1 = | z 2 | γ cos ( γ arg z 2 ) - γ δ arg z 2 + 2 π j, Open image in new window.

By Theorem 3.1, the equality (3.3) is equivalent to Equality (3.4).

It is easy to see that the equality (2.6) is equivalent to the equality (2.3).